{"id":134573,"date":"2024-09-01T21:33:47","date_gmt":"2024-09-01T21:33:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=134573"},"modified":"2024-09-01T21:35:12","modified_gmt":"2024-09-01T21:35:12","slug":"what-is-the-least-common-denominator-for-the-fractions-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/01\/what-is-the-least-common-denominator-for-the-fractions-below\/","title":{"rendered":"What is the least common denominator for the fractions below"},"content":{"rendered":"\n<p>What is the least common denominator for the fractions below? (Round the answer to the nearest integer)<\/p>\n\n\n\n<p>1\/2, 2\/3, 4\/5<\/p>\n\n\n\n<p>A.<br>30<\/p>\n\n\n\n<p>B.<br>25<\/p>\n\n\n\n<p>C.<br>7<\/p>\n\n\n\n<p>D.<br>19<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the least common denominator (LCD) for the fractions 1\/2, 2\/3, and 4\/5, you need to determine the least common multiple (LCM) of the denominators 2, 3, and 5. Here\u2019s a step-by-step explanation:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-Step Solution<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify the Denominators:<\/strong> The denominators of the fractions are 2, 3, and 5.<\/li>\n\n\n\n<li><strong>Prime Factorization:<\/strong>\n<ul class=\"wp-block-list\">\n<li>2 is a prime number, so its prime factorization is simply 2.<\/li>\n\n\n\n<li>3 is also a prime number, so its prime factorization is 3.<\/li>\n\n\n\n<li>5 is another prime number, so its prime factorization is 5.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Find the Least Common Multiple (LCM):<\/strong> To find the LCM, you need to take each prime number that appears in the factorization of the denominators at the highest power it appears. Here are the prime factorizations again:<ul><li>2 = 2^1<\/li><li>3 = 3^1<\/li><li>5 = 5^1<\/li><\/ul>The LCM will be the product of these primes raised to their highest powers:LCM=21\u00d731\u00d751\\text{LCM} = 2^1 \\times 3^1 \\times 5^1LCM=21\u00d731\u00d751 LCM=2\u00d73\u00d75\\text{LCM} = 2 \\times 3 \\times 5LCM=2\u00d73\u00d75 LCM=30\\text{LCM} = 30LCM=30<\/li>\n\n\n\n<li><strong>Verification:<\/strong> To ensure that 30 is indeed the least common multiple:<ul><li>30 \u00f7 2 = 15 (an integer)<\/li><li>30 \u00f7 3 = 10 (an integer)<\/li><li>30 \u00f7 5 = 6 (an integer)<\/li><\/ul>Since 30 is divisible by all the original denominators, it is indeed the least common multiple.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The least common denominator for the fractions 1\/2, 2\/3, and 4\/5 is <strong>30<\/strong>. Therefore, the correct answer is:<\/p>\n\n\n\n<p><strong>A. 30<\/strong><\/p>\n\n\n\n<p>This LCD allows us to compare or combine these fractions easily by converting them to equivalent fractions with a common denominator.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the least common denominator for the fractions below? (Round the answer to the nearest integer) 1\/2, 2\/3, 4\/5 A.30 B.25 C.7 D.19 The Correct answer and Explanation is: To find the least common denominator (LCD) for the fractions 1\/2, 2\/3, and 4\/5, you need to determine the least common multiple (LCM) of the [&hellip;]<\/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-134573","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/134573","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=134573"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/134573\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=134573"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=134573"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=134573"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}