What is the Least Common Multiple of 37344 and 37359?

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 37344 and 37359 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37344 and 37359, than apply into the LCM equation.

GCF(37344,37359) = 3
LCM(37344,37359) = ( 37344 × 37359) / 3
LCM(37344,37359) = 1395134496 / 3
LCM(37344,37359) = 465044832

Least Common Multiple (LCM) of 37344 and 37359 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37344 and 37359. First we will calculate the prime factors of 37344 and 37359.

Prime Factorization of 37344

Prime Factorization of 37359

Now multiplying the highest exponent prime factors to calculate the LCM of 37344 and 37359.

LCM(37344,37359) = 2⁵ × 3² × 389¹ × 7¹ × 593¹
LCM(37344,37359) = 465044832