{"id":20,"date":"2022-04-12T11:50:21","date_gmt":"2022-04-12T11:50:21","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=20"},"modified":"2025-07-30T10:37:28","modified_gmt":"2025-07-30T10:37:28","slug":"a-6-lowest-common-multiple","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/a-6-lowest-common-multiple\/","title":{"rendered":"A.6 Lowest common multiple"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Lowest common multiple<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Class-7-A.6-__Lowest-common-multiple__.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-869a5c0b6b78055316c8d0186252dcbd\" style=\"color:#74008b\"><strong>key notes :<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>What is the Lowest Common Multiple?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Lowest Common Multiple (LCM)<\/strong> is the smallest number that is a multiple of two or more numbers. It is the first number that both of the given numbers divide into without leaving a remainder.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Key Concepts<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Multiple:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Definition:<\/strong> A number that can be divided by another number exactly.<\/li>\n\n\n\n<li><strong>Example:<\/strong> Multiples of 4 are 4, 8, 12, 16, 20, etc.<\/li>\n<\/ul>\n\n\n\n<p><strong>Common Multiple:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Definition:<\/strong> A number that is a multiple of each of the given numbers.<\/li>\n\n\n\n<li><strong>Example:<\/strong> Common multiples of 4 and 6 are 12, 24, 36, etc.<\/li>\n<\/ul>\n\n\n\n<p><strong>Lowest Common Multiple:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Definition:<\/strong> The smallest number that is a multiple of all given numbers.<\/li>\n\n\n\n<li><strong>Example:<\/strong> For 4 and 6, the LCM is 12.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\"><\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>How to Find the LCM<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-large-font-size\">There are different methods to find the LCM:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>1. Listing Multiples Method<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>List the Multiples of Each Number:<\/strong><\/p>\n\n\n\n<p>Find several multiples for each number<\/p>\n\n\n\n<p><strong>Example:<\/strong> For 4 and 6:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiples of 4: 4, 8, 12, 16, 20, 24, &#8230;<\/li>\n\n\n\n<li>Multiples of 6: 6, 12, 18, 24, 30, 36, &#8230;<\/li>\n<\/ul>\n\n\n\n<p><strong>Find the Smallest Common Multiple:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Identify the smallest number that appears in both lists.<\/li>\n\n\n\n<li><strong>LCM:<\/strong> 12<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\"><\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>2. Prime Factorisation Method<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Prime Factorise Each Number:<\/strong><\/p>\n\n\n\n<p>Break each number into prime factors.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4 = 2\u00b2<\/li>\n\n\n\n<li>6 = 2 \u00d7 3<\/li>\n<\/ul>\n\n\n\n<p><strong>Take the Highest Power of Each Prime:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Find the highest power of all prime factors involved.<\/li>\n\n\n\n<li><strong>LCM: 2\u00b2 \u00d7 3 = 12<\/strong><\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\"><\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>3. Using the HCF to Find LCM<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Find the HCF of the Numbers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use the HCF method (Listing Factors or Prime Factorisation).<\/li>\n<\/ul>\n\n\n\n<p><strong>Use the Formula:<\/strong><\/p>\n\n\n\n<p>LCM={Product&nbsp;of&nbsp;the&nbsp;Numbers}\u200b  \/ HCF<\/p>\n\n\n\n<p><strong>Example:<\/strong> For 4 and 6:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Product of Numbers: 4\u00d76=24<\/li>\n\n\n\n<li>HCF of 4 and 6: 2<\/li>\n\n\n\n<li><strong>LCM: 24 \/2 =12<\/strong><\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\"><\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Examples<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Find the LCM of 8 and 12:<\/strong><\/p>\n\n\n\n<p><strong>Listing Multiples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Multiples of 8:<\/strong> 8, 16, 24, 32, 40, 48, &#8230;<\/li>\n\n\n\n<li><strong>Multiples of 12: <\/strong>12, 24, 36, 48, 60, &#8230;<\/li>\n<\/ul>\n\n\n\n<p><strong>LCM:<\/strong> 24<\/p>\n\n\n\n<p><strong>Prime Factorisation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>8 = 2\u00b3<\/li>\n\n\n\n<li>12 = 2\u00b2 \u00d7 3<\/li>\n<\/ul>\n\n\n\n<p>Highest Powers: 2\u00b3 \u00d7 3 = 24<\/p>\n\n\n\n<p><strong>Find the LCM of 9 and 15:<\/strong><\/p>\n\n\n\n<p><strong>Listing Multiples:<\/strong><\/p>\n\n\n\n<p>Multiples of 9: 9, 18, 27, 36, 45, &#8230;<\/p>\n\n\n\n<p>Multiples of 15: 15, 30, 45, 60, 75, &#8230;<\/p>\n\n\n\n<p><strong>LCM:<\/strong> 45<\/p>\n\n\n\n<p><strong>Prime Factorisation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>9 = 3\u00b2<\/li>\n\n\n\n<li>15 = 3 \u00d7 5<\/li>\n\n\n\n<li>Highest Powers: 3\u00b2 \u00d7 5 = 45<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\"><\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Why LCM is Useful<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Scheduling Events:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Helps in finding when two events will occur together again.<\/li>\n<\/ul>\n\n\n\n<p><strong>Solving Problems:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Useful in problems related to repeating patterns or syncing events.<\/li>\n<\/ul>\n\n\n\n<p><strong>Adding or Subtracting Fractions:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Helps in finding a common denominator.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\"><\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Practice Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Find the LCM of 5 and 7.<\/li>\n\n\n\n<li>Find the LCM of 10 and 15.<\/li>\n\n\n\n<li>Find the LCM of 14 and 21.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Visual Representation<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Example: LCM of 4 and 6<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"> <strong>Listing Multiples:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code has-normal-font-size\"><code>Multiples of 4: 4, 8, 12, 16, 20, 24, ...\nMultiples of 6: 6, 12, 18, 24, 30, 36, ...<\/code><\/pre>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Common Multiples:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code has-normal-font-size\"><code>12, 24, 36, ...\nLowest Common Multiple: 12<\/code><\/pre>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Prime Factorisation:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code has-normal-font-size\"><code>4 = 2\u00b2\n6 = 2 \u00d7 3\nLCM = 2\u00b2 \u00d7 3 = 12<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-normal-font-size wp-elements-88040258bb930de625092d26376937bd\" style=\"color:#000060\"><strong>Additional Notes<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>LCM vs. HCF:<\/strong> LCM is the smallest number that can be divided by both numbers, while HCF is the largest number that can divide both numbers.<\/li>\n\n\n\n<li><strong>LCM and Multiples:<\/strong> LCM is always a multiple of each of the numbers you\u2019re finding it for.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f4e98f\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-background-background-color has-text-color has-background has-link-color wp-elements-4bb318ae6d520d6cebf22b85d6ac022a\" style=\"color:#b00012\"><strong>What is the lowest common multiple of 4 and 12?<\/strong><\/p>\n\n\n\n<p>Write the prime factorisation for each number.<\/p>\n\n\n\n<p>4 = 2 \u00d7 2<br>12 = 2 \u00d7 2 \u00d7 3<\/p>\n\n\n\n<p>Repeat each prime factor the most number of times it appears in any of the prime factorisations above.<\/p>\n\n\n\n<p>The most the factor 2 appears is twice.<\/p>\n\n\n\n<p>The most the factor 3 appears is once.<\/p>\n\n\n\n<p>So, multiply:<\/p>\n\n\n\n<p>2 \u00d7 2 \u00d7 3 = 12<br>The lowest common multiple of 4 and 12 is&nbsp;<strong>12<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#c5fdc9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-background-background-color has-text-color has-background has-link-color wp-elements-a82ddd57e5a6dea3d35c53fef7445a00\" style=\"color:#b00012\"><strong>What is the lowest common multiple of 6 and 12?<\/strong><\/p>\n\n\n\n<p>Write the prime factorisation for each number.<\/p>\n\n\n\n<p>6 = 2 \u00d7 3<br>12 = 2 \u00d7 2 \u00d7 3<\/p>\n\n\n\n<p>Repeat each prime factor the most number of times it appears in any of the prime factorisations above.<\/p>\n\n\n\n<p>The most the factor 2 appears is twice.<\/p>\n\n\n\n<p>The most the factor 3 appears is once.<\/p>\n\n\n\n<p>So, multiply:<\/p>\n\n\n\n<p>2 \u00d7 2 \u00d7 3 = 12<br>The lowest common multiple of 6 and 12 is&nbsp;<strong>12<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#98f0fa\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-background-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-f815e2c9a8463978e42f7a4529ca53b2\" style=\"color:#b00012\"><strong>What is the lowest common multiple of 8 and 12?<\/strong><\/p>\n\n\n\n<p>Write the prime factorisation for each number.<\/p>\n\n\n\n<p>8 = 2 \u00d7 2 \u00d7 2<br>12 = 2 \u00d7 2 \u00d7 3<\/p>\n\n\n\n<p>Repeat each prime factor the most number of times it appears in any of the prime factorisations above.<\/p>\n\n\n\n<p>The most the factor 2 appears is three times.<\/p>\n\n\n\n<p>The most the factor 3 appears is once.<\/p>\n\n\n\n<p>So, multiply:<\/p>\n\n\n\n<p>2 \u00d7 2 \u00d7 2 \u00d7 3 = 24<br>The lowest common multiple of 8 and 12 is&nbsp;<strong>24<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84312\/036\/391\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-2.png\" alt=\"\" class=\"wp-image-8420\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-2.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-2-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/78076\/832\/289\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-2.png\" alt=\"\" class=\"wp-image-8421\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-2.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-2-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Lowest common multiple key notes : What is the Lowest Common Multiple? Lowest Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. It is the first number that both of the given numbers divide into without leaving a remainder. Key Concepts Multiple: Common Multiple: Lowest Common Multiple: How<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/a-6-lowest-common-multiple\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.6 Lowest common multiple&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-20","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/20","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=20"}],"version-history":[{"count":27,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/20\/revisions"}],"predecessor-version":[{"id":20957,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/20\/revisions\/20957"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=20"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}