What is the Least Common Multiple of 108 and 126?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 108 and 126 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 108 and 126, than apply into the LCM equation.

GCF(108,126) = 18
LCM(108,126) = ( 108 × 126) / 18
LCM(108,126) = 13608 / 18
LCM(108,126) = 756

Least Common Multiple (LCM) of 108 and 126 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 108 and 126. First we will calculate the prime factors of 108 and 126.

Prime Factorization of 108

Prime Factorization of 126

Now multiplying the highest exponent prime factors to calculate the LCM of 108 and 126.

LCM(108,126) = 2² × 3³ × 7¹
LCM(108,126) = 756