What is the Least Common Multiple of 1000 and 1009?

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 1000 and 1009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1000 and 1009, than apply into the LCM equation.

GCF(1000,1009) = 1
LCM(1000,1009) = ( 1000 × 1009) / 1
LCM(1000,1009) = 1009000 / 1
LCM(1000,1009) = 1009000

Least Common Multiple (LCM) of 1000 and 1009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1009. First we will calculate the prime factors of 1000 and 1009.

Prime Factorization of 1000

Prime Factorization of 1009

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1009.

LCM(1000,1009) = 2³ × 5³ × 1009¹
LCM(1000,1009) = 1009000