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693 (number) - Wikipedia
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Available in 16 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-16" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">16 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/693_(%C4%8D%C3%ADslo)" title="693 (číslo) – Czech" lang="cs" hreflang="cs" data-title="693 (číslo)" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/693_(n%C3%B9mer)" title="693 (nùmer) – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="693 (nùmer)" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/693_(numero)" title="693 (numero) – Italian" lang="it" hreflang="it" data-title="693 (numero)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Mia_sita_tisini_na_tatu" title="Mia sita tisini na tatu – Swahili" lang="sw" hreflang="sw" data-title="Mia sita tisini na tatu" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/693_(nonm)" title="693 (nonm) – Haitian Creole" lang="ht" hreflang="ht" data-title="693 (nonm)" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/693_(sz%C3%A1m)" title="693 (szám) – Hungarian" lang="hu" hreflang="hu" data-title="693 (szám)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/693_(nombor)" title="693 (nombor) – Malay" lang="ms" hreflang="ms" data-title="693 (nombor)" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mni mw-list-item"><a href="https://mni.wikipedia.org/wiki/%EA%AF%B6%EA%AF%B9%EA%AF%B3" title="꯶꯹꯳ – Manipuri" lang="mni" hreflang="mni" data-title="꯶꯹꯳" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="Manipuri" class="interlanguage-link-target"><span>ꯃꯤꯇꯩ ꯂꯣꯟ</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/693" title="693 – Japanese" lang="ja" hreflang="ja" data-title="693" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/693_(son)" title="693 (son) – Uzbek" lang="uz" hreflang="uz" data-title="693 (son)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-nso mw-list-item"><a href="https://nso.wikipedia.org/wiki/693_(nomoro)" title="693 (nomoro) – Northern Sotho" lang="nso" hreflang="nso" data-title="693 (nomoro)" data-language-autonym="Sesotho sa Leboa" data-language-local-name="Northern Sotho" class="interlanguage-link-target"><span>Sesotho sa Leboa</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%A6%D9%A9%D9%A3_(%DA%98%D9%85%D8%A7%D8%B1%DB%95)" title="٦٩٣ (ژمارە) – Central Kurdish" lang="ckb" hreflang="ckb" data-title="٦٩٣ (ژمارە)" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/693_(tal)" title="693 (tal) – Swedish" lang="sv" hreflang="sv" data-title="693 (tal)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/693_(%D1%81%D0%B0%D0%BD)" title="693 (сан) – Tatar" lang="tt" hreflang="tt" data-title="693 (сан)" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/693_(%D8%B9%D8%AF%D8%AF)" title="693 (عدد) – Urdu" lang="ur" hreflang="ur" data-title="693 (عدد)" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/693" title="693 – Cantonese" lang="yue" hreflang="yue" data-title="693" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q3265860#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/693_(number)" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:693_(number)" rel="discussion" title="Discuss improvements to the 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id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/693_(number)" title="Special:EditPage/693 (number)">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22693%22+number">"693" number</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22693%22+number+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22693%22+number&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22693%22+number+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22693%22+number">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22693%22+number&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">August 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div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox" style="line-height: 1.0em"><tbody><tr><th colspan="2" class="infobox-above" style="font-size: 150%"><table style="width:100%; margin:0"><tbody><tr> <td style="width:15%; text-align:left; white-space: nowrap; font-size:smaller"><a href="/wiki/692_(number)" class="mw-redirect" title="692 (number)">← 692 </a></td> <td style="width:70%; padding-left:1em; padding-right:1em; text-align: center;">693</td> <td style="width:15%; text-align:right; white-space: nowrap; font-size:smaller"><a href="/wiki/694_(number)" class="mw-redirect" title="694 (number)"> 694 →</a></td> </tr></tbody></table></th></tr><tr><td colspan="2" class="infobox-subheader" style="font-size:100%;"><div style="text-align:center;"> </div><div style="text-align:center;"> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"><ul><li><a href="/wiki/List_of_numbers" title="List of numbers">List of numbers</a></li><li><a href="/wiki/Integer" title="Integer">Integers</a></li></ul></div></div><div style="text-align:center;"><a href="/wiki/Negative_number" title="Negative number">←</a> <a href="/wiki/0" title="0">0</a> <a href="/wiki/100_(number)" class="mw-redirect" title="100 (number)">100</a> <a href="/wiki/200_(number)" title="200 (number)">200</a> <a href="/wiki/300_(number)" title="300 (number)">300</a> <a href="/wiki/400_(number)" title="400 (number)">400</a> <a href="/wiki/500_(number)" title="500 (number)">500</a> <a href="/wiki/600_(number)" title="600 (number)">600</a> <a href="/wiki/700_(number)" title="700 (number)">700</a> <a href="/wiki/800_(number)" title="800 (number)">800</a> <a href="/wiki/900_(number)" title="900 (number)">900</a> <a href="/wiki/1000_(number)" title="1000 (number)">→</a></div></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Cardinal_numeral" title="Cardinal numeral">Cardinal</a></th><td class="infobox-data">six hundred ninety-three</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Ordinal_numeral" title="Ordinal numeral">Ordinal</a></th><td class="infobox-data">693rd<br />(six hundred ninety-third)</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Factorization" title="Factorization">Factorization</a></th><td class="infobox-data">3<sup>2</sup> × 7 × 11</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numeral</a></th><td class="infobox-data">ΧϞΓ´</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Roman_numerals" title="Roman numerals">Roman numeral</a></th><td class="infobox-data">DCXCIII</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Binary_number" title="Binary number">Binary</a></th><td class="infobox-data">1010110101<sub>2</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Ternary_numeral_system" title="Ternary numeral system">Ternary</a></th><td class="infobox-data">221200<sub>3</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Senary" title="Senary">Senary</a></th><td class="infobox-data">3113<sub>6</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Octal" title="Octal">Octal</a></th><td class="infobox-data">1265<sub>8</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Duodecimal" title="Duodecimal">Duodecimal</a></th><td class="infobox-data">499<sub>12</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Hexadecimal" title="Hexadecimal">Hexadecimal</a></th><td class="infobox-data">2B5<sub>16</sub></td></tr></tbody></table> <p><b>693 (six hundred [and] ninety-three)</b> is the <a href="/wiki/Natural_number" title="Natural number">natural number</a> following <a href="/wiki/692_(number)" class="mw-redirect" title="692 (number)">692</a> and preceding <a href="/wiki/694_(number)" class="mw-redirect" title="694 (number)">694</a>. </p> <div class="mw-heading mw-heading2"><h2 id="In_mathematics">In mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=693_(number)&action=edit&section=1" title="Edit section: In mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>693 has twelve divisors: 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, and 693. Thus, 693 is tied with <a href="/wiki/315_(number)" class="mw-redirect" title="315 (number)">315</a> for the highest number of divisors for any odd natural number below 900. The smallest positive odd integer with more divisors is 945, which has 16 divisors. Consequently, 945 is also the smallest odd <a href="/wiki/Abundant_number" title="Abundant number">abundant number</a>, having an abundancy index of 1920/945 ≈ 2.03175. </p><p>693 appears as the first three digits after the decimal point in the decimal form for the <a href="/wiki/Natural_logarithm_of_2" title="Natural logarithm of 2">natural logarithm of 2</a>. To 10 digits, this number is 0.<b>693</b>1471805. As a result, if an event has a constant <a href="/wiki/Probability" title="Probability">probability</a> of 0.1% of occurring, 693 is the smallest number of trials that must be performed for there to be at least a 50% chance that the event occurs at least once. More generally, for any probability p, the probability that the event occurs at least once in a sample of n items, assuming the items are independent, is given by the following formula: </p><p>1 − (1 − p)<sup>n</sup> </p><p>For p = 10<sup>−3</sup> = 0.001, plugging in n = 692 gives, to four decimal places, 0.4996, while n = 693 yields 0.5001. </p><p>693 is the <a href="/wiki/Lowest_common_multiple" class="mw-redirect" title="Lowest common multiple">lowest common multiple</a> of 7, 9, and 11. Multiplying 693 by 5 gives 3465, the smallest positive integer divisible by 3, 5, 7, 9, and 11.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>693 is a palindrome in bases 32, 62, 76, 98, 230, and 692. It is also a palindrome in binary: 1010110101. </p><p>The reciprocal of 693 has a period of six: <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">693</span></span>⁠</span> = 0.<span style="text-decoration:overline;">001443</span>. </p><p>693 is a triangular matchstick number.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=693_(number)&action=edit&section=2" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://oeis.org/A025547">"Least common multiple of 1,3,5,...,2n-1"</a>. OEIS Foundation.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Least+common+multiple+of+1%2C3%2C5%2C...%2C2n-1.&rft.pub=OEIS+Foundation&rft_id=https%3A%2F%2Foeis.org%2FA025547&rfr_id=info%3Asid%2Fen.wikipedia.org%3A693+%28number%29" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSloane_"A045943"" class="citation web cs1"><a href="/wiki/Neil_Sloane" title="Neil Sloane">Sloane, N. J. A.</a> (ed.). <a rel="nofollow" class="external text" href="https://oeis.org/A045943">"Sequence A045943"</a>. <i>The <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">On-Line Encyclopedia of Integer Sequences</a></i>. OEIS Foundation<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-05-31</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+On-Line+Encyclopedia+of+Integer+Sequences&rft.atitle=Sequence%26%23x20%3BA045943&rft_id=https%3A%2F%2Foeis.org%2FA045943&rfr_id=info%3Asid%2Fen.wikipedia.org%3A693+%28number%29" class="Z3988"></span></span> </li> </ol></div></div> <!-- NewPP limit report Parsed by mw‐web.codfw.main‐f69cdc8f6‐dfwpk Cached time: 20241122152429 Cache expiry: 2592000 Reduced expiry: false Complications: [vary‐revision‐sha1] CPU time usage: 0.289 seconds Real time usage: 0.374 seconds Preprocessor visited node count: 1228/1000000 Post‐expand include size: 28031/2097152 bytes Template argument size: 739/2097152 bytes Highest expansion depth: 13/100 Expensive parser function count: 4/500 Unstrip recursion depth: 1/20 Unstrip post‐expand size: 13239/5000000 bytes Lua time usage: 0.173/10.000 seconds Lua memory usage: 4278722/52428800 bytes Number of Wikibase entities loaded: 0/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 349.452 1 -total 46.11% 161.135 1 Template:Infobox_number 29.73% 103.889 1 Template:Reflist 29.07% 101.596 1 Template:Infobox_number/box 28.15% 98.376 1 Template:Infobox 23.58% 82.409 2 Template:Cite_web 20.35% 71.110 1 Template:Refimprove 16.19% 56.576 1 Template:Ambox 16.03% 56.009 1 Template:Short_description 10.60% 37.039 1 Template:Infobox_number/range --> <!-- Saved in parser cache with key enwiki:pcache:idhash:11670070-0!canonical and timestamp 20241122152429 and revision id 1107315103. 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