What is the Least Common Multiple of 40 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 40 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 40 and 1000, than apply into the LCM equation.

GCF(40,1000) = 40
LCM(40,1000) = ( 40 × 1000) / 40
LCM(40,1000) = 40000 / 40
LCM(40,1000) = 1000

Least Common Multiple (LCM) of 40 and 1000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 1000. First we will calculate the prime factors of 40 and 1000.

Prime Factorization of 40

Prime Factorization of 1000

Now multiplying the highest exponent prime factors to calculate the LCM of 40 and 1000.

LCM(40,1000) = 2³ × 5³
LCM(40,1000) = 1000