What is the Least Common Multiple of 54306 and 54312?

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 54306 and 54312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54306 and 54312, than apply into the LCM equation.

GCF(54306,54312) = 6
LCM(54306,54312) = ( 54306 × 54312) / 6
LCM(54306,54312) = 2949467472 / 6
LCM(54306,54312) = 491577912

Least Common Multiple (LCM) of 54306 and 54312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54306 and 54312. First we will calculate the prime factors of 54306 and 54312.

Prime Factorization of 54306

Prime Factorization of 54312

Now multiplying the highest exponent prime factors to calculate the LCM of 54306 and 54312.

LCM(54306,54312) = 2³ × 3² × 7¹ × 431¹ × 31¹ × 73¹
LCM(54306,54312) = 491577912