What is the Least Common Multiple of 12004 and 12024?

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 12004 and 12024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12004 and 12024, than apply into the LCM equation.

GCF(12004,12024) = 4
LCM(12004,12024) = ( 12004 × 12024) / 4
LCM(12004,12024) = 144336096 / 4
LCM(12004,12024) = 36084024

Least Common Multiple (LCM) of 12004 and 12024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12004 and 12024. First we will calculate the prime factors of 12004 and 12024.

Prime Factorization of 12004

Prime Factorization of 12024

Now multiplying the highest exponent prime factors to calculate the LCM of 12004 and 12024.

LCM(12004,12024) = 2³ × 3001¹ × 3² × 167¹
LCM(12004,12024) = 36084024