What is the Least Common Multiple of 2304 and 2314?

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 2304 and 2314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2304 and 2314, than apply into the LCM equation.

GCF(2304,2314) = 2
LCM(2304,2314) = ( 2304 × 2314) / 2
LCM(2304,2314) = 5331456 / 2
LCM(2304,2314) = 2665728

Least Common Multiple (LCM) of 2304 and 2314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2304 and 2314. First we will calculate the prime factors of 2304 and 2314.

Prime Factorization of 2304

Prime Factorization of 2314

Now multiplying the highest exponent prime factors to calculate the LCM of 2304 and 2314.

LCM(2304,2314) = 2⁸ × 3² × 13¹ × 89¹
LCM(2304,2314) = 2665728