What is the Least Common Multiple of 12000 and 12009?

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 12000 and 12009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12000 and 12009, than apply into the LCM equation.

GCF(12000,12009) = 3
LCM(12000,12009) = ( 12000 × 12009) / 3
LCM(12000,12009) = 144108000 / 3
LCM(12000,12009) = 48036000

Least Common Multiple (LCM) of 12000 and 12009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12000 and 12009. First we will calculate the prime factors of 12000 and 12009.

Prime Factorization of 12000

Prime Factorization of 12009

Now multiplying the highest exponent prime factors to calculate the LCM of 12000 and 12009.

LCM(12000,12009) = 2⁵ × 3¹ × 5³ × 4003¹
LCM(12000,12009) = 48036000