What is the Least Common Multiple of 1000 and 1012?

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 1012 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 1012, than apply into the LCM equation.

GCF(1000,1012) = 4
LCM(1000,1012) = ( 1000 × 1012) / 4
LCM(1000,1012) = 1012000 / 4
LCM(1000,1012) = 253000

Least Common Multiple (LCM) of 1000 and 1012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1012. First we will calculate the prime factors of 1000 and 1012.

Prime Factorization of 1000

Prime Factorization of 1012

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1012.

LCM(1000,1012) = 2³ × 5³ × 11¹ × 23¹
LCM(1000,1012) = 253000