What is the Least Common Multiple of 57108 and 57120?

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 57108 and 57120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57108 and 57120, than apply into the LCM equation.

GCF(57108,57120) = 12
LCM(57108,57120) = ( 57108 × 57120) / 12
LCM(57108,57120) = 3262008960 / 12
LCM(57108,57120) = 271834080

Least Common Multiple (LCM) of 57108 and 57120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57108 and 57120. First we will calculate the prime factors of 57108 and 57120.

Prime Factorization of 57108

Prime Factorization of 57120

Now multiplying the highest exponent prime factors to calculate the LCM of 57108 and 57120.

LCM(57108,57120) = 2⁵ × 3¹ × 4759¹ × 5¹ × 7¹ × 17¹
LCM(57108,57120) = 271834080