What is the Least Common Multiple of 864 and 870?

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 870 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 870, than apply into the LCM equation.

GCF(864,870) = 6
LCM(864,870) = ( 864 × 870) / 6
LCM(864,870) = 751680 / 6
LCM(864,870) = 125280

Least Common Multiple (LCM) of 864 and 870 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 864 and 870. First we will calculate the prime factors of 864 and 870.

Prime Factorization of 864

Prime Factorization of 870

Now multiplying the highest exponent prime factors to calculate the LCM of 864 and 870.

LCM(864,870) = 2⁵ × 3³ × 5¹ × 29¹
LCM(864,870) = 125280