What is the Least Common Multiple (L.C.M) of two or more numbers?

The least common multiple which is shortened as (L.C.M) of two or more numbers is the smallest counting number that is a multiple of each of the giving numbers.

For example, let us see how to find the L.C.M of 3, 4 and 6.

Set of multiples of 3 = {3, 6, 9, 12, 15, 18, 21, 24 ...}

Set of multiples of 4 = {4, 8, 12, 16, 20, 24 ...}

Set of multiples of 6 = {6, 12, 18, 24, 30, 36 ...}

Go ahead find the Set of Common Multiples = {12, 24, 36 ...}, therefore the L.C.M of 3, 4 and 6 is 12. The L.C.M can also be found using Prime Factorization.

For instance if we want to find the L.C.M of 12 and 16,

12        =          2 x 2 x 3          =          2² x 3

16        =          2 x 2 x 2 x 2    =          2⁴

            To find the L.C.M, we need the prime factors whose product is a multiple of both 12 and 16. In this case, students will need each of the different from both factorization and also each to the highest power in which it occurs in either factorization. Hence the L.C.M of 12 and 16 is 2⁴ x 3 = 16 x 3 = 48.

            If a pair of numbers is relatively prime their H.C.F would be 1 but their L.C.M will be given by the product of the numbers. For example, the numbers 5 and 7 are relatively prime hence, the H.C.F of 5 and 7 is 1 and the L.C.M of 5 and 7 is given by 5 x 7 = 35.

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