What is the Least Common Multiple of 312 and 321?

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 321 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 321, than apply into the LCM equation.

GCF(312,321) = 3
LCM(312,321) = ( 312 × 321) / 3
LCM(312,321) = 100152 / 3
LCM(312,321) = 33384

Least Common Multiple (LCM) of 312 and 321 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 312 and 321. First we will calculate the prime factors of 312 and 321.

Prime Factorization of 312

Prime Factorization of 321

Now multiplying the highest exponent prime factors to calculate the LCM of 312 and 321.

LCM(312,321) = 2³ × 3¹ × 13¹ × 107¹
LCM(312,321) = 33384