What is the Least Common Multiple of 87200 and 87216?

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 87200 and 87216 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 87200 and 87216, than apply into the LCM equation.

GCF(87200,87216) = 16
LCM(87200,87216) = ( 87200 × 87216) / 16
LCM(87200,87216) = 7605235200 / 16
LCM(87200,87216) = 475327200

Least Common Multiple (LCM) of 87200 and 87216 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 87200 and 87216. First we will calculate the prime factors of 87200 and 87216.

Prime Factorization of 87200

Prime Factorization of 87216

Now multiplying the highest exponent prime factors to calculate the LCM of 87200 and 87216.

LCM(87200,87216) = 2⁵ × 5² × 109¹ × 3¹ × 23¹ × 79¹
LCM(87200,87216) = 475327200