What is the Least Common Multiple of 39075 and 39084?

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 39075 and 39084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39075 and 39084, than apply into the LCM equation.

GCF(39075,39084) = 3
LCM(39075,39084) = ( 39075 × 39084) / 3
LCM(39075,39084) = 1527207300 / 3
LCM(39075,39084) = 509069100

Least Common Multiple (LCM) of 39075 and 39084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39075 and 39084. First we will calculate the prime factors of 39075 and 39084.

Prime Factorization of 39075

Prime Factorization of 39084

Now multiplying the highest exponent prime factors to calculate the LCM of 39075 and 39084.

LCM(39075,39084) = 3¹ × 5² × 521¹ × 2² × 3257¹
LCM(39075,39084) = 509069100