What is the Least Common Multiple of 3000 and 3012?

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 3000 and 3012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3000 and 3012, than apply into the LCM equation.

GCF(3000,3012) = 12
LCM(3000,3012) = ( 3000 × 3012) / 12
LCM(3000,3012) = 9036000 / 12
LCM(3000,3012) = 753000

Least Common Multiple (LCM) of 3000 and 3012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3000 and 3012. First we will calculate the prime factors of 3000 and 3012.

Prime Factorization of 3000

Prime Factorization of 3012

Now multiplying the highest exponent prime factors to calculate the LCM of 3000 and 3012.

LCM(3000,3012) = 2³ × 3¹ × 5³ × 251¹
LCM(3000,3012) = 753000