What is the Least Common Multiple of 57306 and 57312?

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 57306 and 57312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57306 and 57312, than apply into the LCM equation.

GCF(57306,57312) = 6
LCM(57306,57312) = ( 57306 × 57312) / 6
LCM(57306,57312) = 3284321472 / 6
LCM(57306,57312) = 547386912

Least Common Multiple (LCM) of 57306 and 57312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57306 and 57312. First we will calculate the prime factors of 57306 and 57312.

Prime Factorization of 57306

Prime Factorization of 57312

Now multiplying the highest exponent prime factors to calculate the LCM of 57306 and 57312.

LCM(57306,57312) = 2⁵ × 3² × 9551¹ × 199¹
LCM(57306,57312) = 547386912