What is the Least Common Multiple of 18000 and 18012?

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 18012 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 18012, than apply into the LCM equation.

GCF(18000,18012) = 12
LCM(18000,18012) = ( 18000 × 18012) / 12
LCM(18000,18012) = 324216000 / 12
LCM(18000,18012) = 27018000

Least Common Multiple (LCM) of 18000 and 18012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18000 and 18012. First we will calculate the prime factors of 18000 and 18012.

Prime Factorization of 18000

Prime Factorization of 18012

Now multiplying the highest exponent prime factors to calculate the LCM of 18000 and 18012.

LCM(18000,18012) = 2⁴ × 3² × 5³ × 19¹ × 79¹
LCM(18000,18012) = 27018000