What is the Least Common Multiple of 54900 and 54912?

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 54900 and 54912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54900 and 54912, than apply into the LCM equation.

GCF(54900,54912) = 12
LCM(54900,54912) = ( 54900 × 54912) / 12
LCM(54900,54912) = 3014668800 / 12
LCM(54900,54912) = 251222400

Least Common Multiple (LCM) of 54900 and 54912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54900 and 54912. First we will calculate the prime factors of 54900 and 54912.

Prime Factorization of 54900

Prime Factorization of 54912

Now multiplying the highest exponent prime factors to calculate the LCM of 54900 and 54912.

LCM(54900,54912) = 2⁷ × 3² × 5² × 61¹ × 11¹ × 13¹
LCM(54900,54912) = 251222400