{"id":156350,"date":"2022-03-26T01:39:32","date_gmt":"2022-03-25T20:09:32","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/lcm-of-two-numbers\/"},"modified":"2025-06-20T14:53:43","modified_gmt":"2025-06-20T09:23:43","slug":"lcm-of-two-numbers","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/lcm-of-two-numbers\/","title":{"rendered":"LCM Of Two Numbers"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-of-two-numbers\/#What_is_the_Least_Common_Multiple_LCM\" title=\"What is the Least Common Multiple (LCM)?\">What is the Least Common Multiple (LCM)?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-of-two-numbers\/#How_to_Find_LCM_of_Two_Numbers\" title=\"How to Find LCM of Two Numbers?\">How to Find LCM of Two Numbers?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-of-two-numbers\/#Listing_Multiples_or_Brute_Force_Method_of_Finding_LCM\" title=\"Listing Multiples or Brute Force Method of Finding LCM\">Listing Multiples or Brute Force Method of Finding LCM<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-of-two-numbers\/#Prime_Factorization_Method_of_Finding_LCM\" title=\"Prime Factorization Method of Finding LCM\">Prime Factorization Method of Finding LCM<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-of-two-numbers\/#Division_Method_or_Ladder_Method_of_Finding_LCM\" title=\"Division Method or Ladder Method of Finding LCM\">Division Method or Ladder Method of Finding LCM<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-of-two-numbers\/#GCD_or_GCF_Method_of_Finding_LCM\" title=\"GCD or GCF Method of Finding LCM\">GCD or GCF Method of Finding LCM<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-of-two-numbers\/#Solved_Examples\" title=\"Solved Examples\">Solved Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-of-two-numbers\/#Difference_between_GCF_LCM\" title=\"Difference between GCF &amp; LCM\">Difference between GCF &amp; LCM<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_the_Least_Common_Multiple_LCM\"><\/span>What is the Least Common Multiple (LCM)?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The least common multiple (LCM) is the smallest number that is divisible by each of two or more numbers. The LCM can be found by listing the multiples of each number and finding the smallest number that is listed multiple times. For example, the LCM of 12 and 18 is 36 because the multiples of 12 are 12, 24, 36, 48, and 60, and the multiples of 18 are 18, 36, 54, 72, and 90. The LCM of 15 and 30 is 60 because the multiples of 15 are 15, 30, 45, 60, and 75, and the multiples of 30 are 30, 60, 90, 120, and 150.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156349 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/lcm-of-two-numbers.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/lcm-of-two-numbers.jpg?v=1648238971 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/lcm-of-two-numbers-300x212.jpg?v=1648238971 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Find_LCM_of_Two_Numbers\"><\/span>How to Find LCM of Two Numbers?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are 4 main methods to calculate the least common multiple of 2 numbers. These methods are:<\/p>\n<ul>\n<li>Listing Multiples or Brute Force Method<\/li>\n<li>Prime Factorization Method<\/li>\n<li>Division Method or Ladder Method<\/li>\n<li>GCD or GCF Method<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Listing_Multiples_or_Brute_Force_Method_of_Finding_LCM\"><\/span>Listing Multiples or Brute Force Method of Finding LCM<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In this method, the multiples of each number are listed until the first common multiple is found. Consider the example of 4 and 10. For this method, the multiples of 4 and 10 are to be listed.<\/p>\n<p>Multiples of 4: 4, 8, 12, 16, <strong>20<\/strong>, 24, 28<\/p>\n<p>Multiples of 10: 10, <strong>20<\/strong>, 30, 40<\/p>\n<p>Here, the number 20 is the first common multiple of both 4 and 10. So, the LCM of 4, 10 is 20.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Prime_Factorization_Method_of_Finding_LCM\"><\/span>Prime Factorization Method of Finding LCM<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The prime factorization is one of the most common ways of finding LCM. To find the LCM of two numbers 30 and 45, the steps are as follows:<\/p>\n<p><strong>Step 1:<\/strong> To first list the <strong>prime factors<\/strong> of each number.<\/p>\n<p>30 = 2 \u00d7 3 \u00d7 5<br \/>\n45 = 3 \u00d7 3 \u00d7 5<\/p>\n<p><strong>Step 2: <\/strong>Next multiply each factor the <strong>maximum number of times<\/strong> it occurs in either number.<\/p>\n<p>If the same factor occurs more than once in both numbers, then multiply the factor the maximum number of times it occurs.<\/p>\n<p>The occurrence of Numbers in the above example:<\/p>\n<p><strong>2<\/strong>: one time<br \/>\n<strong>3<\/strong>: two times<br \/>\n<strong>5<\/strong>: one time<br \/>\nLCM = 2 \u00d7 3 \u00d7 3 \u00d7 5 = 90<\/p>\n<p>After calculating the LCM, always check to be sure your answer can be divided evenly by both numbers.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Division_Method_or_Ladder_Method_of_Finding_LCM\"><\/span>Division Method or Ladder Method of Finding LCM<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p align=\"justify\">In this method, the two numbers are simultaneously divided with prime numbers until the division is even. When there are no more primes that evenly divide into both numbers, multiply the divisors to get the LCM. For example, consider 4 and 10 as two<\/p>\n<div id=\"attachment_1149939\" class=\"wp-caption alignnone\">\n<p><img loading=\"lazy\" class=\"wp-image-1149939 size-medium\" title=\"Division Method or Ladder Method of Finding LCM\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/maths\/2016\/08\/17054206\/prime-number-or-1.jpg\" alt=\"Division Method or Ladder Method of Finding LCM\" width=\"133\" height=\"210\" \/><\/p>\n<p class=\"wp-caption-text\">Division Method or Ladder Method of Finding LCM<\/p>\n<\/div>\n<p>Here, the LCM of 24, 15 will be 2\u00d72\u00d72\u00d73\u00d75=23\u00d73\u00d75=120<\/p>\n<h3><span class=\"ez-toc-section\" id=\"GCD_or_GCF_Method_of_Finding_LCM\"><\/span>GCD or GCF Method of Finding LCM<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p align=\"justify\">This method is used only when the greatest common factor of two numbers is given. The formula used to find the LCM using the GCF or GCD is:<\/p>\n<p>L.C.M. = a\u00d7b\/ gcd(a,b)<\/p>\n<p>For example, for 15 and 24, the GCF will be 3. So, the LCM will be (15 \u00d7 24) \/ 3 = 3.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Examples\"><\/span>Solved Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Example 1<\/strong>: Find the L.C.M of 18 and 24 by using the division method?<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<div class=\"table-responsive\">\n<table class=\"table-bordered\">\n<tbody>\n<tr>\n<td>2<\/td>\n<td>18<\/td>\n<td>24<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>9<\/td>\n<td>12<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>9<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>9<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>3<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>For numbers 18 and 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 = 72 is the LCM.<\/p>\n<p><strong>Example 2<\/strong>: Find the Least Common Multiples of these sets of numbers: 3, 9, 21.<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: List the <strong>prime factors<\/strong> of each.<br \/>\n3: 3<br \/>\n9: 3 \u00d7 3<br \/>\n21: 3 \u00d7 7<\/p>\n<p>Step 2: Multiply each factor the <strong>maximum number of times<\/strong> it occurs in any of the numbers.<\/p>\n<p>The occurrence of Numbers in the above example:<\/p>\n<p>3: two times<\/p>\n<p>7: one time<\/p>\n<p>3 x 3 x 7 = 63<\/p>\n<p>9 has two 3s, and 21 has one 7, so we multiply 3 two times, and 7 once.<\/p>\n<p>This gives us 63, the lowest number that can be divided evenly by 3, 9, and 21.<\/p>\n<p><strong>Example 3:<\/strong> Find the Least common factor of 12, 80.<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: List the prime factors of each.<br \/>\n12: 2 \u00d7 2 \u00d7 3<br \/>\n80: 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 5<\/p>\n<p>Step 2:<br \/>\nMultiply each factor the maximum number of times it occurs in either number.<\/p>\n<p>Step 3:<\/p>\n<p>The occurrence of Numbers in the above example:<\/p>\n<p>2: 4 times<\/p>\n<p>3: 1 time<\/p>\n<p>5: 1 time<\/p>\n<p>2 x 2 x 2 x 2 x 3 x 5 =240<\/p>\n<p>12 has one 3, and 80 has four 2\u2019s and one 5, so we multiply 2 four times, 3 once, and five once.<\/p>\n<p>This gives us 240, the lowest number that can be divided by both 12 and 80.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Difference_between_GCF_LCM\"><\/span>Difference between GCF &amp; LCM<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>GCF is the Greatest Common Factor and LCM is the Least Common Multiple.<\/p>\n<p>GCF is the largest number that is a factor of both numbers. LCM is the smallest number that is a multiple of both numbers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the Least Common Multiple (LCM)? The least common multiple (LCM) is the smallest number that is divisible by [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"LCM Of Two Numbers","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn LCM Of Two Numbers topic of Maths in details explained by subject experts on infinitylearn.com. 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