What is the Least Common Multiple of 12304 and 12324?

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 12304 and 12324 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12304 and 12324, than apply into the LCM equation.

GCF(12304,12324) = 4
LCM(12304,12324) = ( 12304 × 12324) / 4
LCM(12304,12324) = 151634496 / 4
LCM(12304,12324) = 37908624

Least Common Multiple (LCM) of 12304 and 12324 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12304 and 12324. First we will calculate the prime factors of 12304 and 12324.

Prime Factorization of 12304

Prime Factorization of 12324

Now multiplying the highest exponent prime factors to calculate the LCM of 12304 and 12324.

LCM(12304,12324) = 2⁴ × 769¹ × 3¹ × 13¹ × 79¹
LCM(12304,12324) = 37908624