What is the Least Common Multiple of 23184 and 23200?

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 23184 and 23200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23184 and 23200, than apply into the LCM equation.

GCF(23184,23200) = 16
LCM(23184,23200) = ( 23184 × 23200) / 16
LCM(23184,23200) = 537868800 / 16
LCM(23184,23200) = 33616800

Least Common Multiple (LCM) of 23184 and 23200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23184 and 23200. First we will calculate the prime factors of 23184 and 23200.

Prime Factorization of 23184

Prime Factorization of 23200

Now multiplying the highest exponent prime factors to calculate the LCM of 23184 and 23200.

LCM(23184,23200) = 2⁵ × 3² × 7¹ × 23¹ × 5² × 29¹
LCM(23184,23200) = 33616800