# CLASS-7FINDING LCM BY PRIME FACTORIZATION METHOD

Finding Lowest Common Multiple (LCM)

The lowest common multiple (LCM) of two or more numbers is the smallest of the common multiple of those numbers. There are two methods of finding LCM – 1) Prime Factorization method and 2) Division method

Method of finding LCM via Prime Factorization method –

Split or express each number as a product of prime factors then take each prime factors as many times as the greatest number of times it appears in any one of the prime factorization of the numbers and the product of the prime factors in step 2 is the LCM of the numbers

Example.1-

Find the LCM of 84 and 112

Ans.)

84 = 2 X 3 X 7 X 2         112 =  2 X 2 X 7 X 2 X 2

The maximum number of times that 2 occurs in the prime factorization of either of the numbers is 4 times, 7 occurs as a prime factor only once, and also 3 occurs as a prime factor only once.

Therefore the required LCM = 2 X 2 X 2 X 2 X 3 X 7 = 336   (Ans.)

Example.2 -

Find the LCM of 72, 56  & 96

72 = 2 X 3 X 3 X 2 X 2 ;      56 = 2 X 2 X 2 X 7 ;

96 =  3 X 2 X 2 X 2 X 2 X 2

From above, we can observe that the maximum number of times 2 occurs in the prime factorization of either of the numbers is 5 times, 3 occurs as a prime factor is maximum 2 times and 7 occurs once

Therefore required LCM is = 2 X 2 X 2 X 2 X 2 X 3 X 3 X 7 = 2016  (Ans.)