What is the Least Common Multiple of 18000 and 18009?

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 18000 and 18009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18000 and 18009, than apply into the LCM equation.

GCF(18000,18009) = 9
LCM(18000,18009) = ( 18000 × 18009) / 9
LCM(18000,18009) = 324162000 / 9
LCM(18000,18009) = 36018000

Least Common Multiple (LCM) of 18000 and 18009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18000 and 18009. First we will calculate the prime factors of 18000 and 18009.

Prime Factorization of 18000

Prime Factorization of 18009

Now multiplying the highest exponent prime factors to calculate the LCM of 18000 and 18009.

LCM(18000,18009) = 2⁴ × 3³ × 5³ × 23¹ × 29¹
LCM(18000,18009) = 36018000