What is the Least Common Multiple of 6072 and 6084?

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 6072 and 6084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6072 and 6084, than apply into the LCM equation.

GCF(6072,6084) = 12
LCM(6072,6084) = ( 6072 × 6084) / 12
LCM(6072,6084) = 36942048 / 12
LCM(6072,6084) = 3078504

Least Common Multiple (LCM) of 6072 and 6084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6072 and 6084. First we will calculate the prime factors of 6072 and 6084.

Prime Factorization of 6072

Prime Factorization of 6084

Now multiplying the highest exponent prime factors to calculate the LCM of 6072 and 6084.

LCM(6072,6084) = 2³ × 3² × 11¹ × 23¹ × 13²
LCM(6072,6084) = 3078504