What is the Least Common Multiple of 54675 and 54684?

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 54684 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 54684, than apply into the LCM equation.

GCF(54675,54684) = 9
LCM(54675,54684) = ( 54675 × 54684) / 9
LCM(54675,54684) = 2989847700 / 9
LCM(54675,54684) = 332205300

Least Common Multiple (LCM) of 54675 and 54684 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54675 and 54684. First we will calculate the prime factors of 54675 and 54684.

Prime Factorization of 54675

Prime Factorization of 54684

Now multiplying the highest exponent prime factors to calculate the LCM of 54675 and 54684.

LCM(54675,54684) = 3⁷ × 5² × 2² × 7² × 31¹
LCM(54675,54684) = 332205300