What is the Least Common Multiple of 72585 and 72600?

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 72585 and 72600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72585 and 72600, than apply into the LCM equation.

GCF(72585,72600) = 15
LCM(72585,72600) = ( 72585 × 72600) / 15
LCM(72585,72600) = 5269671000 / 15
LCM(72585,72600) = 351311400

Least Common Multiple (LCM) of 72585 and 72600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72585 and 72600. First we will calculate the prime factors of 72585 and 72600.

Prime Factorization of 72585

Prime Factorization of 72600

Now multiplying the highest exponent prime factors to calculate the LCM of 72585 and 72600.

LCM(72585,72600) = 3² × 5² × 1613¹ × 2³ × 11²
LCM(72585,72600) = 351311400