What is the Least Common Multiple of 375 and 384?

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 375 and 384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 375 and 384, than apply into the LCM equation.

GCF(375,384) = 3
LCM(375,384) = ( 375 × 384) / 3
LCM(375,384) = 144000 / 3
LCM(375,384) = 48000

Least Common Multiple (LCM) of 375 and 384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 375 and 384. First we will calculate the prime factors of 375 and 384.

Prime Factorization of 375

Prime Factorization of 384

Now multiplying the highest exponent prime factors to calculate the LCM of 375 and 384.

LCM(375,384) = 3¹ × 5³ × 2⁷
LCM(375,384) = 48000