What is the Least Common Multiple of 37152 and 37164?

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 37152 and 37164 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37152 and 37164, than apply into the LCM equation.

GCF(37152,37164) = 12
LCM(37152,37164) = ( 37152 × 37164) / 12
LCM(37152,37164) = 1380716928 / 12
LCM(37152,37164) = 115059744

Least Common Multiple (LCM) of 37152 and 37164 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37152 and 37164. First we will calculate the prime factors of 37152 and 37164.

Prime Factorization of 37152

Prime Factorization of 37164

Now multiplying the highest exponent prime factors to calculate the LCM of 37152 and 37164.

LCM(37152,37164) = 2⁵ × 3³ × 43¹ × 19¹ × 163¹
LCM(37152,37164) = 115059744