What is the Least Common Multiple of 6000 and 6012?

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 6000 and 6012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6000 and 6012, than apply into the LCM equation.

GCF(6000,6012) = 12
LCM(6000,6012) = ( 6000 × 6012) / 12
LCM(6000,6012) = 36072000 / 12
LCM(6000,6012) = 3006000

Least Common Multiple (LCM) of 6000 and 6012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6000 and 6012. First we will calculate the prime factors of 6000 and 6012.

Prime Factorization of 6000

Prime Factorization of 6012

Now multiplying the highest exponent prime factors to calculate the LCM of 6000 and 6012.

LCM(6000,6012) = 2⁴ × 3² × 5³ × 167¹
LCM(6000,6012) = 3006000