What is the Least Common Multiple of 300 and 675?

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 300 and 675 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 300 and 675, than apply into the LCM equation.

GCF(300,675) = 75
LCM(300,675) = ( 300 × 675) / 75
LCM(300,675) = 202500 / 75
LCM(300,675) = 2700

Least Common Multiple (LCM) of 300 and 675 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 300 and 675. First we will calculate the prime factors of 300 and 675.

Prime Factorization of 300

Prime Factorization of 675

Now multiplying the highest exponent prime factors to calculate the LCM of 300 and 675.

LCM(300,675) = 2² × 3³ × 5²
LCM(300,675) = 2700