What is the Least Common Multiple of 2300 and 2312?

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 2300 and 2312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2300 and 2312, than apply into the LCM equation.

GCF(2300,2312) = 4
LCM(2300,2312) = ( 2300 × 2312) / 4
LCM(2300,2312) = 5317600 / 4
LCM(2300,2312) = 1329400

Least Common Multiple (LCM) of 2300 and 2312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2300 and 2312. First we will calculate the prime factors of 2300 and 2312.

Prime Factorization of 2300

Prime Factorization of 2312

Now multiplying the highest exponent prime factors to calculate the LCM of 2300 and 2312.

LCM(2300,2312) = 2³ × 5² × 23¹ × 17²
LCM(2300,2312) = 1329400