What is the Least Common Multiple of 357 and 375?

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 357 and 375 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 357 and 375, than apply into the LCM equation.

GCF(357,375) = 3
LCM(357,375) = ( 357 × 375) / 3
LCM(357,375) = 133875 / 3
LCM(357,375) = 44625

Least Common Multiple (LCM) of 357 and 375 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 357 and 375. First we will calculate the prime factors of 357 and 375.

Prime Factorization of 357

Prime Factorization of 375

Now multiplying the highest exponent prime factors to calculate the LCM of 357 and 375.

LCM(357,375) = 3¹ × 7¹ × 17¹ × 5³
LCM(357,375) = 44625