What is the Least Common Multiple of 39306 and 39312?

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 39306 and 39312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39306 and 39312, than apply into the LCM equation.

GCF(39306,39312) = 6
LCM(39306,39312) = ( 39306 × 39312) / 6
LCM(39306,39312) = 1545197472 / 6
LCM(39306,39312) = 257532912

Least Common Multiple (LCM) of 39306 and 39312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39306 and 39312. First we will calculate the prime factors of 39306 and 39312.

Prime Factorization of 39306

Prime Factorization of 39312

Now multiplying the highest exponent prime factors to calculate the LCM of 39306 and 39312.

LCM(39306,39312) = 2⁴ × 3³ × 6551¹ × 7¹ × 13¹
LCM(39306,39312) = 257532912