What is the Least Common Multiple of 1000 and 1020?

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 1020 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 1020, than apply into the LCM equation.

GCF(1000,1020) = 20
LCM(1000,1020) = ( 1000 × 1020) / 20
LCM(1000,1020) = 1020000 / 20
LCM(1000,1020) = 51000

Least Common Multiple (LCM) of 1000 and 1020 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1020. First we will calculate the prime factors of 1000 and 1020.

Prime Factorization of 1000

Prime Factorization of 1020

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1020.

LCM(1000,1020) = 2³ × 5³ × 3¹ × 17¹
LCM(1000,1020) = 51000