What is the Least Common Multiple of 72375 and 72384?

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 72375 and 72384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72375 and 72384, than apply into the LCM equation.

GCF(72375,72384) = 3
LCM(72375,72384) = ( 72375 × 72384) / 3
LCM(72375,72384) = 5238792000 / 3
LCM(72375,72384) = 1746264000

Least Common Multiple (LCM) of 72375 and 72384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72375 and 72384. First we will calculate the prime factors of 72375 and 72384.

Prime Factorization of 72375

Prime Factorization of 72384

Now multiplying the highest exponent prime factors to calculate the LCM of 72375 and 72384.

LCM(72375,72384) = 3¹ × 5³ × 193¹ × 2⁶ × 13¹ × 29¹
LCM(72375,72384) = 1746264000