What is the Least Common Multiple of 954 and 972?

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 954 and 972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 954 and 972, than apply into the LCM equation.

GCF(954,972) = 18
LCM(954,972) = ( 954 × 972) / 18
LCM(954,972) = 927288 / 18
LCM(954,972) = 51516

Least Common Multiple (LCM) of 954 and 972 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 954 and 972. First we will calculate the prime factors of 954 and 972.

Prime Factorization of 954

Prime Factorization of 972

Now multiplying the highest exponent prime factors to calculate the LCM of 954 and 972.

LCM(954,972) = 2² × 3⁵ × 53¹
LCM(954,972) = 51516