What is the Least Common Multiple of 54084 and 54096?

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 54084 and 54096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54084 and 54096, than apply into the LCM equation.

GCF(54084,54096) = 12
LCM(54084,54096) = ( 54084 × 54096) / 12
LCM(54084,54096) = 2925728064 / 12
LCM(54084,54096) = 243810672

Least Common Multiple (LCM) of 54084 and 54096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54084 and 54096. First we will calculate the prime factors of 54084 and 54096.

Prime Factorization of 54084

Prime Factorization of 54096

Now multiplying the highest exponent prime factors to calculate the LCM of 54084 and 54096.

LCM(54084,54096) = 2⁴ × 3¹ × 4507¹ × 7² × 23¹
LCM(54084,54096) = 243810672