What is the Least Common Multiple of 37584 and 37599?

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 37584 and 37599 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37584 and 37599, than apply into the LCM equation.

GCF(37584,37599) = 3
LCM(37584,37599) = ( 37584 × 37599) / 3
LCM(37584,37599) = 1413120816 / 3
LCM(37584,37599) = 471040272

Least Common Multiple (LCM) of 37584 and 37599 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37584 and 37599. First we will calculate the prime factors of 37584 and 37599.

Prime Factorization of 37584

Prime Factorization of 37599

Now multiplying the highest exponent prime factors to calculate the LCM of 37584 and 37599.

LCM(37584,37599) = 2⁴ × 3⁴ × 29¹ × 83¹ × 151¹
LCM(37584,37599) = 471040272