What is the Least Common Multiple of 9075 and 9084?

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 9075 and 9084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9075 and 9084, than apply into the LCM equation.

GCF(9075,9084) = 3
LCM(9075,9084) = ( 9075 × 9084) / 3
LCM(9075,9084) = 82437300 / 3
LCM(9075,9084) = 27479100

Least Common Multiple (LCM) of 9075 and 9084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9075 and 9084. First we will calculate the prime factors of 9075 and 9084.

Prime Factorization of 9075

Prime Factorization of 9084

Now multiplying the highest exponent prime factors to calculate the LCM of 9075 and 9084.

LCM(9075,9084) = 3¹ × 5² × 11² × 2² × 757¹
LCM(9075,9084) = 27479100