{"id":156378,"date":"2022-03-26T01:41:26","date_gmt":"2022-03-25T20:11:26","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/hcf-and-lcm-definition-formula-calculation-methods-solved-examples\/"},"modified":"2025-06-20T14:53:26","modified_gmt":"2025-06-20T09:23:26","slug":"hcf-and-lcm-definition-formula-calculation-methods-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/","title":{"rendered":"HCF and LCM &#8211; Definition, Formula, Calculation, Methods &#038; Solved Examples"},"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-and-hcf\/#What_is_the_Definition_of_LCM_and_HCF\" title=\"What is the Definition of LCM and HCF?\">What is the Definition of LCM and HCF?<\/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-and-hcf\/#What_does_HCF_mean\" title=\"What does HCF mean?\">What does HCF mean?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/#How_is_HCF_calculated\" title=\"How is HCF calculated?\">How is HCF calculated?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/#How_to_calculate_LCM_and_HCF\" title=\"How to calculate LCM and HCF?\">How to calculate LCM and HCF?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/#1_Factorization_Method\" title=\"1. Factorization Method\">1. Factorization Method<\/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-and-hcf\/#2_Gaussian_Elimination_Method\" title=\"2. Gaussian Elimination Method\">2. Gaussian Elimination Method<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/#3_Prime_Factorization_Method_Also_known_as_the_Factor_Tree_Method\" title=\"3. Prime Factorization Method (Also known as the Factor Tree Method)\">3. Prime Factorization Method (Also known as the Factor Tree Method)<\/a><\/li><\/ul><\/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-and-hcf\/#Division_Method\" title=\"Division Method\">Division Method<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/#How_to_find_the_HCF_of_3_Numbers_or_How_to_find_the_Highest_Common_Factor\" title=\"How to find the HCF of 3 Numbers or How to find the Highest Common Factor?\">How to find the HCF of 3 Numbers or How to find the Highest Common Factor?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/#How_is_LCM_Calculated\" title=\"How is LCM Calculated?\">How is LCM Calculated?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/#How_to_find_LCM_by_Prime_Factorization\" title=\"How to find LCM by Prime Factorization?\">How to find LCM by Prime Factorization?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/#How_to_find_LCM_by_Prime_Factorization_using_the_Concept_of_Exponents\" title=\"How to find LCM by Prime Factorization using the Concept of Exponents?\">How to find LCM by Prime Factorization using the Concept of Exponents?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/#Where_are_HCF_and_LCM_used\" title=\"Where are HCF and LCM used?\">Where are HCF and LCM used?<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_the_Definition_of_LCM_and_HCF\"><\/span>What is the Definition of LCM and HCF?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>HCF and LCM &#8211; Definition: The <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/\">LCM<\/a> (Least Common Multiple) is the smallest number that is a multiple of two or more numbers.<\/p>\n<p>The HCF (Highest Common Factor) is the largest number that is a factor of two or more numbers.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156377 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/hcf-and-lcm-definition-formula-calculation-methods-solved-examples.jpg\" alt=\"HCF and LCM - Definition, Formula, Calculation, Methods &amp; Solved Examples\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/hcf-and-lcm-definition-formula-calculation-methods-solved-examples.jpg?v=1648239083 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/hcf-and-lcm-definition-formula-calculation-methods-solved-examples-300x212.jpg?v=1648239083 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_does_HCF_mean\"><\/span>What does HCF mean?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>HCF stands for the Highest Common Factor. The Highest Common Factor is the largest number that is a factor of two or more numbers. The Highest Common Factor can be found by dividing all of the numbers by the largest number that is a factor of all of the numbers.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_is_HCF_calculated\"><\/span>How is HCF calculated?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>HCF is calculated by dividing the largest number by the smallest number.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_calculate_LCM_and_HCF\"><\/span>How to calculate LCM and HCF?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The lowest common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers. The highest common factor (HCF) of two or more numbers is the largest number that is a factor of each of the numbers.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"1_Factorization_Method\"><\/span>1. Factorization Method<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The factorization method is a technique used to solve a system of linear equations. The method works by factoring the coefficients of the equations into a product of linear factors. The factors are then rearranged so that the equations are in standard form and the solution is found by solving the equations.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_Gaussian_Elimination_Method\"><\/span>2. Gaussian Elimination Method<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The Gaussian elimination method is a technique used to solve a system of linear equations. The method works by eliminating variables one at a time until the system is in standard form. The solution is found by solving the equations.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_Prime_Factorization_Method_Also_known_as_the_Factor_Tree_Method\"><\/span>3. Prime Factorization Method (Also known as the Factor Tree Method)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>This is a method for finding the prime factors of a number. It is also called the factor tree method because it uses a tree diagram to organize the prime factors.<\/li>\n<li>To use the prime factorization method, start by writing the number you are trying to factorize vertically. Next, draw a tree diagram with the number at the top and the prime factors below. Write the prime factorization of the number next to the appropriate branch on the tree.<\/li>\n<\/ul>\n<p>Here is an example.<\/p>\n<p>The number 36 can be factorized into the prime factors 6 and 6.<\/p>\n<p>Here is another example.<\/p>\n<p>The number 15 can be factorized into the prime factors 3 and 5.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Division_Method\"><\/span>Division Method<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Let&#8217;s say you have the following list of numbers:<\/p>\n<p>1, 2, 3, 4, 5<\/p>\n<p>We can divide this list into two groups:<\/p>\n<p>1, 2, 3, 4, 5<br \/>\n6, 7, 8, 9, 10<\/p>\n<p>The first group is {1, 2, 3, 4, 5} and the second group is {6, 7, 8, 9, 10}.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_find_the_HCF_of_3_Numbers_or_How_to_find_the_Highest_Common_Factor\"><\/span>How to find the HCF of 3 Numbers or How to find the Highest Common Factor?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Highest Common Factor (HCF) of 3 numbers is the largest number that is a common factor of all 3 numbers.<\/p>\n<p>To find the HCF of 3 numbers, list all of the factors of each number and find the largest number that is a factor of all 3 numbers.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_is_LCM_Calculated\"><\/span>How is LCM Calculated?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>To calculate the LCM, first list all of the multiples of the given number. Next, find the least common multiple (LCM) of all of the multiples. The LCM is the smallest number that is a multiple of all of the given numbers.<\/li>\n<li>For example, the LCM of 4 and 6 is 12. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and 32. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, and 48. The LCM is 12, because it is a multiple of 4 and 6.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"How_to_find_LCM_by_Prime_Factorization\"><\/span>How to find LCM by Prime Factorization?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The LCM can be found by prime factorization. The prime factorization of a number is the decomposition of the number into its prime factors. The prime factors of a number are the numbers that are only divisible by themselves and 1. The LCM can be found by multiplying all of the prime factors of a number together.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"How_to_find_LCM_by_Prime_Factorization_using_the_Concept_of_Exponents\"><\/span>How to find LCM by Prime Factorization using the Concept of Exponents?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The LCM of two numbers can be found by multiplying the prime factors of those numbers and then taking the highest power of each prime factor.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Where_are_HCF_and_LCM_used\"><\/span>Where are HCF and LCM used?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>HCF and LCM are used in a variety of different ways. HCF is used to find the greatest common divisor of two numbers, and LCM is used to find the least common multiple of two numbers. These two operations are important in a variety of different mathematical problems, such as finding the solutions to equations. Additionally, HCF and LCM can be used to simplify fractions and to find the prime factors of a number.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the Definition of LCM and HCF? HCF and LCM &#8211; Definition: The LCM (Least Common Multiple) is the [&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":"HCF and LCM - Definition","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"HCF and LCM - Definition: LCM is smallest number while HCF is largest number that is a factor of two or more numbers.","custom_permalink":"maths\/lcm-and-hcf\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>HCF and LCM - Definition, Formula, Calculation, Methods &amp; Solved Examples<\/title>\n<meta name=\"description\" content=\"HCF and LCM - Definition: LCM is smallest number while HCF is largest number that is a factor of two or more numbers.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/lcm-and-hcf\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"HCF and LCM - 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