What is the Least Common Multiple of 30 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 30 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 30 and 312, than apply into the LCM equation.

GCF(30,312) = 6
LCM(30,312) = ( 30 × 312) / 6
LCM(30,312) = 9360 / 6
LCM(30,312) = 1560

Least Common Multiple (LCM) of 30 and 312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 312. First we will calculate the prime factors of 30 and 312.

Prime Factorization of 30

Prime Factorization of 312

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 312.

LCM(30,312) = 2³ × 3¹ × 5¹ × 13¹
LCM(30,312) = 1560