What is the Least Common Multiple of 87180 and 87200?

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 87180 and 87200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 87180 and 87200, than apply into the LCM equation.

GCF(87180,87200) = 20
LCM(87180,87200) = ( 87180 × 87200) / 20
LCM(87180,87200) = 7602096000 / 20
LCM(87180,87200) = 380104800

Least Common Multiple (LCM) of 87180 and 87200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 87180 and 87200. First we will calculate the prime factors of 87180 and 87200.

Prime Factorization of 87180

Prime Factorization of 87200

Now multiplying the highest exponent prime factors to calculate the LCM of 87180 and 87200.

LCM(87180,87200) = 2⁵ × 3¹ × 5² × 1453¹ × 109¹
LCM(87180,87200) = 380104800