What is the Least Common Multiple of 72384 and 72390?

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 72390 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 72390, than apply into the LCM equation.

GCF(72384,72390) = 6
LCM(72384,72390) = ( 72384 × 72390) / 6
LCM(72384,72390) = 5239877760 / 6
LCM(72384,72390) = 873312960

Least Common Multiple (LCM) of 72384 and 72390 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72384 and 72390. First we will calculate the prime factors of 72384 and 72390.

Prime Factorization of 72384

Prime Factorization of 72390

Now multiplying the highest exponent prime factors to calculate the LCM of 72384 and 72390.

LCM(72384,72390) = 2⁶ × 3¹ × 13¹ × 29¹ × 5¹ × 19¹ × 127¹
LCM(72384,72390) = 873312960