What is the Least Common Multiple of 23700 and 23712?

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 23700 and 23712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23700 and 23712, than apply into the LCM equation.

GCF(23700,23712) = 12
LCM(23700,23712) = ( 23700 × 23712) / 12
LCM(23700,23712) = 561974400 / 12
LCM(23700,23712) = 46831200

Least Common Multiple (LCM) of 23700 and 23712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23700 and 23712. First we will calculate the prime factors of 23700 and 23712.

Prime Factorization of 23700

Prime Factorization of 23712

Now multiplying the highest exponent prime factors to calculate the LCM of 23700 and 23712.

LCM(23700,23712) = 2⁵ × 3¹ × 5² × 79¹ × 13¹ × 19¹
LCM(23700,23712) = 46831200