What is the Least Common Multiple of 2000 and 2009?

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 2009 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 2009, than apply into the LCM equation.

GCF(2000,2009) = 1
LCM(2000,2009) = ( 2000 × 2009) / 1
LCM(2000,2009) = 4018000 / 1
LCM(2000,2009) = 4018000

Least Common Multiple (LCM) of 2000 and 2009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2000 and 2009. First we will calculate the prime factors of 2000 and 2009.

Prime Factorization of 2000

Prime Factorization of 2009

Now multiplying the highest exponent prime factors to calculate the LCM of 2000 and 2009.

LCM(2000,2009) = 2⁴ × 5³ × 7² × 41¹
LCM(2000,2009) = 4018000