{"id":7578,"date":"2021-10-27T17:36:31","date_gmt":"2021-10-27T12:06:31","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7578"},"modified":"2022-10-01T22:41:14","modified_gmt":"2022-10-01T17:11:14","slug":"how-to-find-least-common-multiple-lcm-of-numbers-and-fractions","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/how-to-find-least-common-multiple-lcm-of-numbers-and-fractions\/","title":{"rendered":"How to Find Least Common Multiple (LCM) of Numbers and Fractions"},"content":{"rendered":"

Here you will learn concept of LCM and how to find least common multiple (LCM) of numbers and fractions with examples.<\/p>\n

Let’s begin –<\/p>\n

Concept of LCM<\/h2>\n

Let \\(n_1\\) and \\(n_2\\) be two natural numbers distinct from each other. The smallest natural number n that is exactly divisible by \\(n_1\\) and \\(n_2\\) is called Least Common Multiple (LCM) of \\(n_1\\) and \\(n_2\\) and is designated as LCM(\\(n_1\\), \\(n_2\\)).<\/p>\n

How to Find Least Common Multiple (LCM)<\/h2>\n
\n

(a) Find the standard form of the numbers.<\/p>\n

(b) Write out all the prime factors, which are contained in the standard forms of either of the numbers.<\/p>\n

(c) Raise each of the prime factors listed above to the highest of the powers in which it appears in the standard forms of the numbers.<\/p>\n

(d) The product of results of the previous step will be the LCM of numbers.<\/p>\n<\/blockquote>\n

Note<\/strong> : GCD(\\(n_1\\), \\(n_2\\)).LCM(\\(n_1\\), \\(n_2\\)) = \\(n_1\\).\\(n_2\\)<\/p>\n

i.e. The product of the HCF and LCM equal to the product of the numbers.<\/p>\n

Rule for Finding LCM of Fractions\u00a0<\/h2>\n

LCM of two or more fractions is given by :<\/p>\n

\n

\\(LCM of Numerators\\over HCF of Denominators\\)<\/p>\n<\/blockquote>\n

Example<\/span><\/strong> : Find the LCM of 150, 210, 375.<\/p>\n

Solution<\/span><\/strong> : We have the numbers, 150, 210, 375.<\/p>\n

1). Writing down the standard form of numbers.<\/p>\n

150 = \\(5 \\times 5 \\times 3 \\times 2\\)<\/p>\n

210 = \\(5 \\times 2 \\times 7 \\times 3\\)<\/p>\n

375 = \\(5 \\times 5 \\times 5 \\times 3\\)<\/p>\n

2). Write down all the prime factors that appears at least once in any of the numbers : 5, 3, 2, 7<\/p>\n

3). Raise each of the prime factors to their highest available power (considering each to the numbers).<\/p>\n

Hence, the LCM will be \\(2^1\\times 3^1 \\times 5^3 \\times 7^1\\) = 5250<\/p>\n

Example<\/span><\/strong> : Find the LCM of 50, 75.<\/p>\n

Solution<\/span><\/strong> : We have the numbers, 50, 75<\/p>\n

1). Writing down the standard form of numbers.<\/p>\n

50 = \\(5 \\times 5 \\times 2 \\)<\/p>\n

75 = \\(5 \\times 5 \\times 3\\)<\/p>\n

2). Write down all the prime factors that appears at least once in any of the numbers : 5, 3, 2<\/p>\n

3). Raise each of the prime factors to their highest available power (considering each to the numbers).<\/p>\n

\u00a0Hence, the LCM will be \\(5^2\\times 3^1 \\times 2^1\\) = 150<\/p>\n\n\n

\n
Next – How to Find Greatest Common Divisor (GCD or HCF)<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – What are Rational and Irrational Numbers with Examples ?<\/a><\/div>\n<\/div>\n\n\n\n

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

Here you will learn concept of LCM and how to find least common multiple (LCM) of numbers and fractions with examples. Let’s begin – Concept of LCM Let \\(n_1\\) and \\(n_2\\) be two natural numbers distinct from each other. The smallest natural number n that is exactly divisible by \\(n_1\\) and \\(n_2\\) is called Least …<\/p>\n

How to Find Least Common Multiple (LCM) of Numbers and Fractions<\/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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[62],"tags":[501,502,500],"yoast_head":"\nHow to Find Least Common Multiple (LCM) of Numbers and Fractions<\/title>\n<meta name=\"description\" content=\"In this post you will learn concept of LCM and how to find least common multiple 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