What is the Least Common Multiple of 57072 and 57084?

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 57072 and 57084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57072 and 57084, than apply into the LCM equation.

GCF(57072,57084) = 12
LCM(57072,57084) = ( 57072 × 57084) / 12
LCM(57072,57084) = 3257898048 / 12
LCM(57072,57084) = 271491504

Least Common Multiple (LCM) of 57072 and 57084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57072 and 57084. First we will calculate the prime factors of 57072 and 57084.

Prime Factorization of 57072

Prime Factorization of 57084

Now multiplying the highest exponent prime factors to calculate the LCM of 57072 and 57084.

LCM(57072,57084) = 2⁴ × 3¹ × 29¹ × 41¹ × 67¹ × 71¹
LCM(57072,57084) = 271491504