What is the Least Common Multiple of 72306 and 72312?

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 72306 and 72312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72306 and 72312, than apply into the LCM equation.

GCF(72306,72312) = 6
LCM(72306,72312) = ( 72306 × 72312) / 6
LCM(72306,72312) = 5228591472 / 6
LCM(72306,72312) = 871431912

Least Common Multiple (LCM) of 72306 and 72312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72306 and 72312. First we will calculate the prime factors of 72306 and 72312.

Prime Factorization of 72306

Prime Factorization of 72312

Now multiplying the highest exponent prime factors to calculate the LCM of 72306 and 72312.

LCM(72306,72312) = 2³ × 3³ × 13¹ × 103¹ × 23¹ × 131¹
LCM(72306,72312) = 871431912