{"id":10387,"date":"2022-04-05T17:30:04","date_gmt":"2022-04-05T12:00:04","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10387"},"modified":"2022-06-04T19:39:41","modified_gmt":"2022-06-04T14:09:41","slug":"find-the-h-c-f-and-l-c-m-of-the-following-integers-by-applying-prime-factorisation-method","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-h-c-f-and-l-c-m-of-the-following-integers-by-applying-prime-factorisation-method\/","title":{"rendered":"Find the H.C.F and L.C.M of the following integers by applying prime factorisation method."},"content":{"rendered":"

Question<\/strong> : Find the H.C.F and L.C.M of the following integers by applying prime factorisation method.<\/p>\n

(i)\u00a0 12, 15, 21<\/p>\n

(ii)\u00a0 17, 23, 29<\/p>\n

(iii)\u00a0 8, 9 and 25<\/p>\n

Solution<\/strong> :<\/p>\n

(i)\u00a0<\/strong>12, 15, 21<\/p>\n

12 = \\(2 \\times 2 \\times 3\\)<\/p>\n

15 = \\(3 \\times 5\\)<\/p>\n

21 = \\(3 \\times 7\\)<\/p>\n

Here 3 is a common prime factor of the given numbers.<\/p>\n

Hence, HCF = 3<\/p>\n

H.C.F. (12, 15, 21) = 3<\/strong><\/p>\n

L.C.M is the product of the prime factors\u00a0 \\(2 \\times 2 \\times 3 \\times 7 \\times 5\\)<\/p>\n

The common factor 3 is repeated three times, so we write 3 only one times in multiplication..<\/p>\n

L.C.M. (12, 15, 21) = 420<\/strong><\/p>\n

(ii)\u00a0<\/strong>17, 23, 29<\/p>\n

H.C.F. There is no common factor as 17, 23, 29 they are prime. Hence, H.C.F is 1.<\/p>\n

L.C.M. is the product of all prime factors 17, 23 and 29.<\/p>\n

\\(17 \\times 23 \\times 29\\) = 11339<\/p>\n

Hence, H.C.F. (17, 23, 29) = 1.<\/strong><\/p>\n

L.C.M (17, 23, 29) = 11339<\/strong><\/p>\n

(iii)\u00a0<\/strong>8, 9 and 25<\/p>\n

First we write the prime factorisation of each of the given numbers.<\/p>\n

8 = \\(2 \\times 2 \\times\\) = \\(2^3\\),<\/p>\n

9 = \\(3 \\times 3\\) = \\(3^2\\)<\/p>\n

25 = \\(5 \\times 5\\) = \\(5^2\\)<\/p>\n

\\(\\therefore\\)\u00a0 L.C.M = \\(2^2 \\times 3^2 \\times 5^2\\) = \\(8 \\times 9 \\times 25\\) = 1800<\/strong><\/p>\n

and H.C.F = 1.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Find the H.C.F and L.C.M of the following integers by applying prime factorisation method. (i)\u00a0 12, 15, 21 (ii)\u00a0 17, 23, 29 (iii)\u00a0 8, 9 and 25 Solution : (i)\u00a012, 15, 21 12 = \\(2 \\times 2 \\times 3\\) 15 = \\(3 \\times 5\\) 21 = \\(3 \\times 7\\) Here 3 is a …<\/p>\n

Find the H.C.F and L.C.M of the following integers by applying prime factorisation method.<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,909],"tags":[],"yoast_head":"\nFind the H.C.F and L.C.M of the following integers by applying prime factorisation method. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/find-the-h-c-f-and-l-c-m-of-the-following-integers-by-applying-prime-factorisation-method\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the H.C.F and L.C.M of the following integers by applying prime factorisation method. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Question : Find the H.C.F and L.C.M of the following integers by applying prime factorisation method. (i)\u00a0 12, 15, 21 (ii)\u00a0 17, 23, 29 (iii)\u00a0 8, 9 and 25 Solution : (i)\u00a012, 15, 21 12 = (2 times 2 times 3) 15 = (3 times 5) 21 = (3 times 7) Here 3 is a … Find the H.C.F and L.C.M of the following integers by applying prime factorisation method. 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(i)\u00a0 12, 15, 21 (ii)\u00a0 17, 23, 29 (iii)\u00a0 8, 9 and 25 Solution : (i)\u00a012, 15, 21 12 = (2 times 2 times 3) 15 = (3 times 5) 21 = (3 times 7) Here 3 is a … Find the H.C.F and L.C.M of the following integers by applying prime factorisation method. 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