What is the Least Common Multiple of 57660 and 57675?

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 57660 and 57675 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57660 and 57675, than apply into the LCM equation.

GCF(57660,57675) = 15
LCM(57660,57675) = ( 57660 × 57675) / 15
LCM(57660,57675) = 3325540500 / 15
LCM(57660,57675) = 221702700

Least Common Multiple (LCM) of 57660 and 57675 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57660 and 57675. First we will calculate the prime factors of 57660 and 57675.

Prime Factorization of 57660

Prime Factorization of 57675

Now multiplying the highest exponent prime factors to calculate the LCM of 57660 and 57675.

LCM(57660,57675) = 2² × 3¹ × 5² × 31² × 769¹
LCM(57660,57675) = 221702700