What is the Least Common Multiple of 57312 and 57321?

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 57312 and 57321 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57312 and 57321, than apply into the LCM equation.

GCF(57312,57321) = 9
LCM(57312,57321) = ( 57312 × 57321) / 9
LCM(57312,57321) = 3285181152 / 9
LCM(57312,57321) = 365020128

Least Common Multiple (LCM) of 57312 and 57321 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57312 and 57321. First we will calculate the prime factors of 57312 and 57321.

Prime Factorization of 57312

Prime Factorization of 57321

Now multiplying the highest exponent prime factors to calculate the LCM of 57312 and 57321.

LCM(57312,57321) = 2⁵ × 3³ × 199¹ × 11¹ × 193¹
LCM(57312,57321) = 365020128