What is the Least Common Multiple of 89856 and 89872?

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 89856 and 89872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 89856 and 89872, than apply into the LCM equation.

GCF(89856,89872) = 16
LCM(89856,89872) = ( 89856 × 89872) / 16
LCM(89856,89872) = 8075538432 / 16
LCM(89856,89872) = 504721152

Least Common Multiple (LCM) of 89856 and 89872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 89856 and 89872. First we will calculate the prime factors of 89856 and 89872.

Prime Factorization of 89856

Prime Factorization of 89872

Now multiplying the highest exponent prime factors to calculate the LCM of 89856 and 89872.

LCM(89856,89872) = 2⁸ × 3³ × 13¹ × 41¹ × 137¹
LCM(89856,89872) = 504721152