What is the Least Common Multiple of 27306 and 27312?

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 27306 and 27312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27306 and 27312, than apply into the LCM equation.

GCF(27306,27312) = 6
LCM(27306,27312) = ( 27306 × 27312) / 6
LCM(27306,27312) = 745781472 / 6
LCM(27306,27312) = 124296912

Least Common Multiple (LCM) of 27306 and 27312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27306 and 27312. First we will calculate the prime factors of 27306 and 27312.

Prime Factorization of 27306

Prime Factorization of 27312

Now multiplying the highest exponent prime factors to calculate the LCM of 27306 and 27312.

LCM(27306,27312) = 2⁴ × 3² × 37¹ × 41¹ × 569¹
LCM(27306,27312) = 124296912