What is the Least Common Multiple of 864 and 875?

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 864 and 875 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 864 and 875, than apply into the LCM equation.

GCF(864,875) = 1
LCM(864,875) = ( 864 × 875) / 1
LCM(864,875) = 756000 / 1
LCM(864,875) = 756000

Least Common Multiple (LCM) of 864 and 875 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 864 and 875. First we will calculate the prime factors of 864 and 875.

Prime Factorization of 864

Prime Factorization of 875

Now multiplying the highest exponent prime factors to calculate the LCM of 864 and 875.

LCM(864,875) = 2⁵ × 3³ × 5³ × 7¹
LCM(864,875) = 756000