{"id":67146,"date":"2026-10-20T09:51:57","date_gmt":"2026-10-20T06:51:57","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=67146"},"modified":"2026-10-20T09:51:57","modified_gmt":"2026-10-20T06:51:57","slug":"lcm-calculator-least-common-multiple","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/lcm-calculator-least-common-multiple\/","title":{"rendered":"LCM Calculator \u2013 Least Common Multiple"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Find the LCM of Whole Numbers<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"67146\" data-favorite-title=\"LCM\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/lcm-calculator-least-common-multiple\/\" data-favorite-excerpt=\"Find the least common multiple and greatest common divisor of 2 to 10 positive integers. Enter numbers separated by commas or spaces to see their prime factorizations and the steps behind the LCM.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-arithmetic\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/mathematics\/lcm-calculator-least-common-multiple\/\" method=\"POST\" class=\"calculator\" id=\"calculator-67146\" data-post=\"67146\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Positive integers<\/label><textarea id=\"field-1\" name=\"positive_integers\">12, 18, 30<\/textarea><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"67146\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Least common multiple (LCM)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Greatest common divisor (GCD)<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Prime factorization of each number<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Highest power of each prime<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-5\"><span class=\"field-title\"><span>Product of the highest powers<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"67146\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span 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class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>LCM Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[\\operatorname{LCM}(a_1,a_2,\\ldots,a_n)=\\prod_{p}p^{\\max\\left(v_p(a_1),v_p(a_2),\\ldots,v_p(a_n)\\right)}\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(a_1,a_2,\\ldots,a_n\\) \u2014 the positive integers entered.<\/li>\n<li>\\(p\\) \u2014 a prime factor of at least one entered number.<\/li>\n<li>\\(v_p(a_i)\\) \u2014 the exponent of \\(p\\) in the prime factorization of \\(a_i\\); it is 0 if \\(p\\) is not a factor.<\/li>\n<\/ul>\n<p>For each prime that appears, take its highest exponent among the entered numbers. Multiplying those prime powers gives the smallest positive integer divisible by every entry.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>LCM \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> find the LCM of the default entries 12, 18, and 30.<\/p>\n<p>Factor each number, then select the highest power of each prime:<\/p>\n<p>\\[12=2^2\\times3,\\qquad18=2\\times3^2,\\qquad30=2\\times3\\times5\\]<\/p>\n<p>\\[\\operatorname{LCM}(12,18,30)=2^2\\times3^2\\times5=4\\times9\\times5=180\\]<\/p>\n<p><strong>Result:<\/strong> the LCM is 180. The calculator also reports a GCD of 6.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>In <strong>Positive integers<\/strong>, enter 2 to 10 numbers separated by commas or spaces. For example, enter <code>12, 18, 30<\/code>.<\/li>\n<li>Read <strong>Least common multiple (LCM)<\/strong> for the smallest positive number divisible by every entry.<\/li>\n<li>Check <strong>Greatest common divisor (GCD)<\/strong> for the largest positive number that divides every entry without a remainder.<\/li>\n<li>Use <strong>Prime factorization of each number<\/strong> to see how each entry breaks down. <strong>Highest power of each prime<\/strong> shows which factors to keep, and <strong>Product of the highest powers<\/strong> shows how they combine to produce the LCM.<\/li>\n<\/ol>\n<h2>What the least common multiple means<\/h2>\n<p>A multiple of a positive integer is that integer multiplied by another whole number. The least common multiple, or LCM, is the smallest positive multiple shared by all the numbers you enter. For instance, 180 is divisible by 12, 18, and 30; no smaller positive integer is divisible by all three. A larger common multiple, such as 360, works too, but it is not the <em>least<\/em> one.<\/p>\n<p>The LCM is useful when quantities must be expressed in compatible units or repeating events must line up. If one event repeats every 12 days and another every 18 days, they coincide every 36 days when they start together. For fractions, the LCM of the denominators provides a least common denominator, making the fractions easier to add or compare.<\/p>\n<p>Prime factorization explains why the calculation works. Each input must divide the result, so the result needs at least as many copies of every prime as the input with the highest exponent. In the example, 18 supplies \\(3^2\\), 12 supplies \\(2^2\\), and 30 supplies \\(5\\). Keeping all three highest powers gives 180. You can inspect an individual number in the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/prime-factorization-calculator\/\">Prime Factorization Calculator<\/a> or use the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/prime-number-checker\/\">Prime Number Checker<\/a> to check whether a factor is prime.<\/p>\n<p>The GCD answers a different question: what is the largest number that divides <em>every<\/em> entry? For 12, 18, and 30, that number is 6. The LCM takes the highest power of each prime needed across the inputs, whereas the GCD keeps only prime powers common to all of them. For two positive numbers \\(a\\) and \\(b\\), you can check the results with \\(\\operatorname{LCM}(a,b)\\times\\operatorname{GCD}(a,b)=a\\times b\\). That identity should not be applied unchanged to three or more numbers.<\/p>\n<h2>Input limits and practical tips<\/h2>\n<ul>\n<li>Enter 2 to 10 positive integers. Each entry must be between 1 and 1,000,000,000,000. Zero, negative numbers, decimals, and fractions are not accepted.<\/li>\n<li>Use commas or spaces <em>between<\/em> entries, not as thousands separators. For example, <code>1000 2500<\/code> represents two numbers, while <code>1,000, 2,500<\/code> is read as four numbers.<\/li>\n<li>Including 1 does not increase the LCM. Repeating an entry does not change either the LCM or GCD.<\/li>\n<li>If the numbers share no prime factor across all entries, their GCD is 1. This does not necessarily mean their LCM is their product: that shortcut requires the numbers to be pairwise coprime.<\/li>\n<li>The LCM can be much larger than any individual input, especially when the entries share few factors. Its size alone is not an error; check the displayed prime powers to see how it was formed.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Find the least common multiple and greatest common divisor of 2 to 10 positive integers. Enter numbers separated by commas or spaces to see their prime factorizations and the steps behind the LCM.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[72],"class_list":["post-67146","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-arithmetic-calculators"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67146","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=67146"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67146\/revisions"}],"predecessor-version":[{"id":67226,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67146\/revisions\/67226"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=67146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=67146"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=67146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}