What is the Least Common Multiple of 72000 and 72009?

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 72000 and 72009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72000 and 72009, than apply into the LCM equation.

GCF(72000,72009) = 9
LCM(72000,72009) = ( 72000 × 72009) / 9
LCM(72000,72009) = 5184648000 / 9
LCM(72000,72009) = 576072000

Least Common Multiple (LCM) of 72000 and 72009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72000 and 72009. First we will calculate the prime factors of 72000 and 72009.

Prime Factorization of 72000

Prime Factorization of 72009

Now multiplying the highest exponent prime factors to calculate the LCM of 72000 and 72009.

LCM(72000,72009) = 2⁶ × 3⁴ × 5³ × 7¹ × 127¹
LCM(72000,72009) = 576072000