What is the Least Common Multiple of 72135 and 72144?

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 72135 and 72144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72135 and 72144, than apply into the LCM equation.

GCF(72135,72144) = 9
LCM(72135,72144) = ( 72135 × 72144) / 9
LCM(72135,72144) = 5204107440 / 9
LCM(72135,72144) = 578234160

Least Common Multiple (LCM) of 72135 and 72144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72135 and 72144. First we will calculate the prime factors of 72135 and 72144.

Prime Factorization of 72135

Prime Factorization of 72144

Now multiplying the highest exponent prime factors to calculate the LCM of 72135 and 72144.

LCM(72135,72144) = 3³ × 5¹ × 7¹ × 229¹ × 2⁴ × 167¹
LCM(72135,72144) = 578234160