What is the Least Common Multiple of 45075 and 45084?

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 45075 and 45084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45075 and 45084, than apply into the LCM equation.

GCF(45075,45084) = 3
LCM(45075,45084) = ( 45075 × 45084) / 3
LCM(45075,45084) = 2032161300 / 3
LCM(45075,45084) = 677387100

Least Common Multiple (LCM) of 45075 and 45084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45075 and 45084. First we will calculate the prime factors of 45075 and 45084.

Prime Factorization of 45075

Prime Factorization of 45084

Now multiplying the highest exponent prime factors to calculate the LCM of 45075 and 45084.

LCM(45075,45084) = 3¹ × 5² × 601¹ × 2² × 13¹ × 17²
LCM(45075,45084) = 677387100