What is the Least Common Multiple of 852 and 864?

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 852 and 864 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 852 and 864, than apply into the LCM equation.

GCF(852,864) = 12
LCM(852,864) = ( 852 × 864) / 12
LCM(852,864) = 736128 / 12
LCM(852,864) = 61344

Least Common Multiple (LCM) of 852 and 864 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 852 and 864. First we will calculate the prime factors of 852 and 864.

Prime Factorization of 852

Prime Factorization of 864

Now multiplying the highest exponent prime factors to calculate the LCM of 852 and 864.

LCM(852,864) = 2⁵ × 3³ × 71¹
LCM(852,864) = 61344