What is the Least Common Multiple of 2000 and 2012?

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 2000 and 2012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2000 and 2012, than apply into the LCM equation.

GCF(2000,2012) = 4
LCM(2000,2012) = ( 2000 × 2012) / 4
LCM(2000,2012) = 4024000 / 4
LCM(2000,2012) = 1006000

Least Common Multiple (LCM) of 2000 and 2012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2000 and 2012. First we will calculate the prime factors of 2000 and 2012.

Prime Factorization of 2000

Prime Factorization of 2012

Now multiplying the highest exponent prime factors to calculate the LCM of 2000 and 2012.

LCM(2000,2012) = 2⁴ × 5³ × 503¹
LCM(2000,2012) = 1006000