What is the Least Common Multiple of 54675 and 54688?

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 54675 and 54688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54675 and 54688, than apply into the LCM equation.

GCF(54675,54688) = 1
LCM(54675,54688) = ( 54675 × 54688) / 1
LCM(54675,54688) = 2990066400 / 1
LCM(54675,54688) = 2990066400

Least Common Multiple (LCM) of 54675 and 54688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54675 and 54688. First we will calculate the prime factors of 54675 and 54688.

Prime Factorization of 54675

Prime Factorization of 54688

Now multiplying the highest exponent prime factors to calculate the LCM of 54675 and 54688.

LCM(54675,54688) = 3⁷ × 5² × 2⁵ × 1709¹
LCM(54675,54688) = 2990066400