What is the Least Common Multiple of 54096 and 54114?

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 54096 and 54114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54096 and 54114, than apply into the LCM equation.

GCF(54096,54114) = 6
LCM(54096,54114) = ( 54096 × 54114) / 6
LCM(54096,54114) = 2927350944 / 6
LCM(54096,54114) = 487891824

Least Common Multiple (LCM) of 54096 and 54114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54096 and 54114. First we will calculate the prime factors of 54096 and 54114.

Prime Factorization of 54096

Prime Factorization of 54114

Now multiplying the highest exponent prime factors to calculate the LCM of 54096 and 54114.

LCM(54096,54114) = 2⁴ × 3¹ × 7² × 23¹ × 29¹ × 311¹
LCM(54096,54114) = 487891824