LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

FINDING 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.)**