What is the Least Common Multiple of 72384 and 72400?

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 72384 and 72400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72384 and 72400, than apply into the LCM equation.

GCF(72384,72400) = 16
LCM(72384,72400) = ( 72384 × 72400) / 16
LCM(72384,72400) = 5240601600 / 16
LCM(72384,72400) = 327537600

Least Common Multiple (LCM) of 72384 and 72400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72384 and 72400. First we will calculate the prime factors of 72384 and 72400.

Prime Factorization of 72384

Prime Factorization of 72400

Now multiplying the highest exponent prime factors to calculate the LCM of 72384 and 72400.

LCM(72384,72400) = 2⁶ × 3¹ × 13¹ × 29¹ × 5² × 181¹
LCM(72384,72400) = 327537600