What is the Least Common Multiple of 8 and 1000?

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 8 and 1000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 1000, than apply into the LCM equation.

GCF(8,1000) = 8
LCM(8,1000) = ( 8 × 1000) / 8
LCM(8,1000) = 8000 / 8
LCM(8,1000) = 1000

Least Common Multiple (LCM) of 8 and 1000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 1000. First we will calculate the prime factors of 8 and 1000.

Prime Factorization of 8

Prime Factorization of 1000

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 1000.

LCM(8,1000) = 2³ × 5³
LCM(8,1000) = 1000