{"id":240818,"date":"2025-07-03T12:08:37","date_gmt":"2025-07-03T12:08:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=240818"},"modified":"2025-07-03T12:08:39","modified_gmt":"2025-07-03T12:08:39","slug":"find-the-lcm-of-each-number-using-prime-factorization","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/find-the-lcm-of-each-number-using-prime-factorization\/","title":{"rendered":"Find the LCM of each number using prime factorization"},"content":{"rendered":"\n

Find the LCM of each number using prime factorization: 35, 75, 50.<\/p>\n\n\n\n

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

To find the Least Common Multiple (LCM)<\/strong> of the numbers 35, 75, and 50<\/strong> using prime factorization<\/strong>, follow these steps:<\/p>\n\n\n\n

Step 1: Prime Factorization of Each Number<\/h3>\n\n\n\n
    \n
  1. 35<\/strong>:
    35 is divisible by 5 (because it ends in 5).
    35 \u00f7 5 = 7.
    So, 35 = 5 \u00d7 7<\/strong>.<\/li>\n\n\n\n
  2. 75<\/strong>:
    75 is divisible by 5 (since it ends in 5).
    75 \u00f7 5 = 15.
    15 is also divisible by 5.
    15 \u00f7 5 = 3.
    So, 75 = 5\u00b2 \u00d7 3<\/strong>.<\/li>\n\n\n\n
  3. 50<\/strong>:
    50 is divisible by 5.
    50 \u00f7 5 = 10.
    10 is divisible by 5 again.
    10 \u00f7 5 = 2.
    So, 50 = 5\u00b2 \u00d7 2<\/strong>.<\/li>\n<\/ol>\n\n\n\n

    Step 2: Identify the Highest Powers of Each Prime Factor<\/h3>\n\n\n\n

    Now, identify the highest powers<\/strong> of each prime factor present in the factorizations:<\/p>\n\n\n\n

      \n
    • Prime factor 2<\/strong>: The highest power is 2\u00b9<\/strong> (from 50).<\/li>\n\n\n\n
    • Prime factor 3<\/strong>: The highest power is 3\u00b9<\/strong> (from 75).<\/li>\n\n\n\n
    • Prime factor 5<\/strong>: The highest power is 5\u00b2<\/strong> (from both 75 and 50).<\/li>\n\n\n\n
    • Prime factor 7<\/strong>: The highest power is 7\u00b9<\/strong> (from 35).<\/li>\n<\/ul>\n\n\n\n

      Step 3: Multiply the Highest Powers Together<\/h3>\n\n\n\n

      To find the LCM, multiply the highest powers of each prime factor:LCM=21\u00d731\u00d752\u00d771LCM = 2\u00b9 \u00d7 3\u00b9 \u00d7 5\u00b2 \u00d7 7\u00b9LCM=21\u00d731\u00d752\u00d771LCM=2\u00d73\u00d725\u00d77LCM = 2 \u00d7 3 \u00d7 25 \u00d7 7LCM=2\u00d73\u00d725\u00d77LCM=2\u00d73=6LCM = 2 \u00d7 3 = 6LCM=2\u00d73=66\u00d725=1506 \u00d7 25 = 1506\u00d725=150150\u00d77=1050150 \u00d7 7 = 1050150\u00d77=1050<\/p>\n\n\n\n

      Final Answer:<\/h3>\n\n\n\n

      The LCM<\/strong> of 35, 75, and 50 is 1050<\/strong>.<\/p>\n\n\n\n

      Explanation:<\/h3>\n\n\n\n
        \n
      • The LCM is the smallest number that is divisible by each of the given numbers.<\/li>\n\n\n\n
      • Using prime factorization, you find the highest powers of each prime factor from all the numbers and multiply them together.<\/li>\n\n\n\n
      • By following this method, you ensure that the LCM will include all factors of each original number without any unnecessary repeats.<\/li>\n<\/ul>\n\n\n\n
        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Find the LCM of each number using prime factorization: 35, 75, 50. The Correct Answer and Explanation is: To find the Least Common Multiple (LCM) of the numbers 35, 75, and 50 using prime factorization, follow these steps: Step 1: Prime Factorization of Each Number Step 2: Identify the Highest Powers of Each Prime Factor […]<\/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-240818","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240818","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=240818"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240818\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240818"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240818"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240818"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}