What is the Least Common Multiple of 57342 and 57360?

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 57342 and 57360 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57342 and 57360, than apply into the LCM equation.

GCF(57342,57360) = 6
LCM(57342,57360) = ( 57342 × 57360) / 6
LCM(57342,57360) = 3289137120 / 6
LCM(57342,57360) = 548189520

Least Common Multiple (LCM) of 57342 and 57360 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57342 and 57360. First we will calculate the prime factors of 57342 and 57360.

Prime Factorization of 57342

Prime Factorization of 57360

Now multiplying the highest exponent prime factors to calculate the LCM of 57342 and 57360.

LCM(57342,57360) = 2⁴ × 3¹ × 19¹ × 503¹ × 5¹ × 239¹
LCM(57342,57360) = 548189520