What is the Least Common Multiple of 312 and 318?

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 312 and 318 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 312 and 318, than apply into the LCM equation.

GCF(312,318) = 6
LCM(312,318) = ( 312 × 318) / 6
LCM(312,318) = 99216 / 6
LCM(312,318) = 16536

Least Common Multiple (LCM) of 312 and 318 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 312 and 318. First we will calculate the prime factors of 312 and 318.

Prime Factorization of 312

Prime Factorization of 318

Now multiplying the highest exponent prime factors to calculate the LCM of 312 and 318.

LCM(312,318) = 2³ × 3¹ × 13¹ × 53¹
LCM(312,318) = 16536