What is the Least Common Multiple of 17304 and 17312?

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 17304 and 17312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17304 and 17312, than apply into the LCM equation.

GCF(17304,17312) = 8
LCM(17304,17312) = ( 17304 × 17312) / 8
LCM(17304,17312) = 299566848 / 8
LCM(17304,17312) = 37445856

Least Common Multiple (LCM) of 17304 and 17312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17304 and 17312. First we will calculate the prime factors of 17304 and 17312.

Prime Factorization of 17304

Prime Factorization of 17312

Now multiplying the highest exponent prime factors to calculate the LCM of 17304 and 17312.

LCM(17304,17312) = 2⁵ × 3¹ × 7¹ × 103¹ × 541¹
LCM(17304,17312) = 37445856