What is the Least Common Multiple of 300 and 312?

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 312 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 312, than apply into the LCM equation.

GCF(300,312) = 12
LCM(300,312) = ( 300 × 312) / 12
LCM(300,312) = 93600 / 12
LCM(300,312) = 7800

Least Common Multiple (LCM) of 300 and 312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 300 and 312. First we will calculate the prime factors of 300 and 312.

Prime Factorization of 300

Prime Factorization of 312

Now multiplying the highest exponent prime factors to calculate the LCM of 300 and 312.

LCM(300,312) = 2³ × 3¹ × 5² × 13¹
LCM(300,312) = 7800