__Factorization method__

In this article we learn “__how to calculate lcm using prime factorization__“. Numbers are factorized to find the __least common multiple__ by the __factorization method__. We will consider this method as set by set.

**First Step – **We do the prime factors of the given numbers.

Example – If we have to find the least common denominator of 7, 14, 24. So first we will find their prime factors.

- Prime prime factors of 8?

The prime factor of 8 is 2 × 2 × 2

- Prime prime factors of 16?

Prime factorization of 16 = 2 x 2 x 2 x 2

- Prime factorization of 24?

Prime factorization of 24 = 2x2x2x3

**Second Step – **In this step we organize the number. Lets keep small numbers first.

Prime factorization of 8 = 2 x2x2

Prime factorization of 16 = 2x2x2x2

Prime factorization of 24 = 2x2x2x3

**Third Step – **After arranging all the numbers the common numbers are chosen.

Prime factorization of 8 = 2 x2x2

Prime factorization of 16 = 2x2x2x2

Prime factorization of 24 = 2x2x2x3

Hence the common number is 2x2x2.

**Fourth Step – **After selecting common numbers, we include the remaining numbers.

Prime factorization of 8 = 2 x2x2

Prime factorization of 16 = 2x2x2x2

Prime factorization of 24 = 2x2x2x3

Hence the remaining number is 2×3.

The product of all numbers and the remaining numbers is the least common multiple of 8, 16, 24.

The least common multiple of 8, 16, 24 = 48.