What is the Least Common Multiple of 37656 and 37664?

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 37656 and 37664 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37656 and 37664, than apply into the LCM equation.

GCF(37656,37664) = 8
LCM(37656,37664) = ( 37656 × 37664) / 8
LCM(37656,37664) = 1418275584 / 8
LCM(37656,37664) = 177284448

Least Common Multiple (LCM) of 37656 and 37664 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37656 and 37664. First we will calculate the prime factors of 37656 and 37664.

Prime Factorization of 37656

Prime Factorization of 37664

Now multiplying the highest exponent prime factors to calculate the LCM of 37656 and 37664.

LCM(37656,37664) = 2⁵ × 3² × 523¹ × 11¹ × 107¹
LCM(37656,37664) = 177284448