{"id":231420,"date":"2025-06-11T06:03:17","date_gmt":"2025-06-11T06:03:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=231420"},"modified":"2025-06-11T06:03:21","modified_gmt":"2025-06-11T06:03:21","slug":"find-the-least-common-multiple-of-12-30-and-32","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/11\/find-the-least-common-multiple-of-12-30-and-32\/","title":{"rendered":"Find the Least Common Multiple of 12, 30, and 32"},"content":{"rendered":"\n

Find the Least Common Multiple of 12, 30, and 32<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The least common multiple (LCM) of 12, 30, and 32 is 480<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The Least Common Multiple (LCM) of a set of numbers is the smallest number that is a multiple of each of the given numbers. To determine the LCM of 12, 30, and 32, we follow a systematic approach using prime factorization.<\/p>\n\n\n\n

Step 1: Prime Factorization<\/h4>\n\n\n\n

We first break each number down into its prime factors:<\/p>\n\n\n\n

    \n
  • 12 = 22\u00d732^2 \\times 3<\/li>\n\n\n\n
  • 30 = 2\u00d73\u00d752 \\times 3 \\times 5<\/li>\n\n\n\n
  • 32 = 252^5<\/li>\n<\/ul>\n\n\n\n

    Step 2: Identifying the Highest Powers of Each Prime Factor<\/h4>\n\n\n\n

    To find the LCM, we take the highest powers of all prime factors present:<\/p>\n\n\n\n

      \n
    • The highest power of 2<\/strong> is 252^5 (from 32).<\/li>\n\n\n\n
    • The highest power of 3<\/strong> is 313^1 (from 12 and 30).<\/li>\n\n\n\n
    • The highest power of 5<\/strong> is 515^1 (from 30).<\/li>\n<\/ul>\n\n\n\n

      Thus, the LCM is found by multiplying the highest powers:<\/p>\n\n\n\n

      LCM=25\u00d731\u00d751LCM = 2^5 \\times 3^1 \\times 5^1<\/p>\n\n\n\n

      LCM=32\u00d73\u00d75=480LCM = 32 \\times 3 \\times 5 = 480<\/p>\n\n\n\n

      Step 3: Confirming Multiples<\/h4>\n\n\n\n

      Now, we check that 480<\/strong> is divisible by 12, 30, and 32:<\/p>\n\n\n\n

        \n
      • 480\u00f712=40480 \\div 12 = 40 \u2705<\/li>\n\n\n\n
      • 480\u00f730=16480 \\div 30 = 16 \u2705<\/li>\n\n\n\n
      • 480\u00f732=15480 \\div 32 = 15 \u2705<\/li>\n<\/ul>\n\n\n\n

        Since 480 is a multiple of all three numbers, it is the correct Least Common Multiple (LCM).<\/strong><\/p>\n\n\n\n

        This method ensures accuracy and is widely used in books and textbooks to find the LCM of multiple numbers efficiently.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Find the Least Common Multiple of 12, 30, and 32 The Correct Answer and Explanation is: The least common multiple (LCM) of 12, 30, and 32 is 480. Explanation: The Least Common Multiple (LCM) of a set of numbers is the smallest number that is a multiple of each of the given numbers. To determine […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-231420","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=231420"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231420\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=231420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=231420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=231420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}