What is the Least Common Multiple of 57084 and 57096?

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 57084 and 57096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57084 and 57096, than apply into the LCM equation.

GCF(57084,57096) = 12
LCM(57084,57096) = ( 57084 × 57096) / 12
LCM(57084,57096) = 3259268064 / 12
LCM(57084,57096) = 271605672

Least Common Multiple (LCM) of 57084 and 57096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57084 and 57096. First we will calculate the prime factors of 57084 and 57096.

Prime Factorization of 57084

Prime Factorization of 57096

Now multiplying the highest exponent prime factors to calculate the LCM of 57084 and 57096.

LCM(57084,57096) = 2³ × 3² × 67¹ × 71¹ × 13¹ × 61¹
LCM(57084,57096) = 271605672