{"id":258097,"date":"2025-07-17T21:42:54","date_gmt":"2025-07-17T21:42:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=258097"},"modified":"2025-07-17T21:42:55","modified_gmt":"2025-07-17T21:42:55","slug":"if-the-lcm-of-two-prime-numbers-is-437-find-one-number-given-that-the-other-is-23","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/17\/if-the-lcm-of-two-prime-numbers-is-437-find-one-number-given-that-the-other-is-23\/","title":{"rendered":"If the LCM of two Prime numbers is 437, Find one number given that the other is 23"},"content":{"rendered":"\n<p>If the LCM of two Prime numbers is 437, Find one number given that the other is 23<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find one of the numbers, we can use the relationship between the Least Common Multiple (LCM) and the numbers involved. The LCM of two numbers is given by the formula:LCM(a,b)=a\u00d7bGCD(a,b)\\text{LCM}(a, b) = \\frac{a \\times b}{\\text{GCD}(a, b)}LCM(a,b)=GCD(a,b)a\u00d7b\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>aaa and bbb are the two numbers.<\/li>\n\n\n\n<li>GCD is the Greatest Common Divisor of the two numbers.<\/li>\n<\/ul>\n\n\n\n<p>Since 23 is a prime number, it only has two divisors: 1 and 23. Therefore, the GCD of 23 and any other prime number (say ppp) will always be 1, because prime numbers don&#8217;t share any divisors other than 1. This simplifies the LCM formula to:LCM(23,p)=23\u00d7p\\text{LCM}(23, p) = 23 \\times pLCM(23,p)=23\u00d7p<\/p>\n\n\n\n<p>We are given that the LCM of the two numbers is 437. Therefore:23\u00d7p=43723 \\times p = 43723\u00d7p=437<\/p>\n\n\n\n<p>To solve for ppp, divide both sides of the equation by 23:p=43723p = \\frac{437}{23}p=23437\u200bp=19p = 19p=19<\/p>\n\n\n\n<p>Thus, the other number is <strong>19<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The LCM of two prime numbers is simply the product of the two numbers since their only common factor is 1.<\/li>\n\n\n\n<li>Given that one number is 23 and the LCM is 437, we divide the LCM by 23 to find the second number.<\/li>\n\n\n\n<li>Therefore, the other number is 19.<\/li>\n<\/ul>\n\n\n\n<p>This solution assumes that both numbers are prime, as indicated in the question.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-869.jpeg\" alt=\"\" class=\"wp-image-258098\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>If the LCM of two Prime numbers is 437, Find one number given that the other is 23 The Correct Answer and Explanation is: To find one of the numbers, we can use the relationship between the Least Common Multiple (LCM) and the numbers involved. The LCM of two numbers is given by the formula:LCM(a,b)=a\u00d7bGCD(a,b)\\text{LCM}(a, [&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-258097","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258097","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=258097"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258097\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258097"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258097"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258097"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}