What is the Least Common Multiple of 6 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 6 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 6 and 126, than apply into the LCM equation.

GCF(6,126) = 6
LCM(6,126) = ( 6 × 126) / 6
LCM(6,126) = 756 / 6
LCM(6,126) = 126

Least Common Multiple (LCM) of 6 and 126 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 126. First we will calculate the prime factors of 6 and 126.

Prime Factorization of 6

Prime Factorization of 126

Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 126.

LCM(6,126) = 2¹ × 3² × 7¹
LCM(6,126) = 126