What is the Least Common Multiple of 1000 and 1007?

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 1007 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 1007, than apply into the LCM equation.

GCF(1000,1007) = 1
LCM(1000,1007) = ( 1000 × 1007) / 1
LCM(1000,1007) = 1007000 / 1
LCM(1000,1007) = 1007000

Least Common Multiple (LCM) of 1000 and 1007 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1007. First we will calculate the prime factors of 1000 and 1007.

Prime Factorization of 1000

Prime Factorization of 1007

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1007.

LCM(1000,1007) = 2³ × 5³ × 19¹ × 53¹
LCM(1000,1007) = 1007000