What is the Least Common Multiple of 90072 and 90084?

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 90072 and 90084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90072 and 90084, than apply into the LCM equation.

GCF(90072,90084) = 12
LCM(90072,90084) = ( 90072 × 90084) / 12
LCM(90072,90084) = 8114046048 / 12
LCM(90072,90084) = 676170504

Least Common Multiple (LCM) of 90072 and 90084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90072 and 90084. First we will calculate the prime factors of 90072 and 90084.

Prime Factorization of 90072

Prime Factorization of 90084

Now multiplying the highest exponent prime factors to calculate the LCM of 90072 and 90084.

LCM(90072,90084) = 2³ × 3⁴ × 139¹ × 7507¹
LCM(90072,90084) = 676170504