What is the Least Common Multiple of 1000 and 1014?

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 1014 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 1014, than apply into the LCM equation.

GCF(1000,1014) = 2
LCM(1000,1014) = ( 1000 × 1014) / 2
LCM(1000,1014) = 1014000 / 2
LCM(1000,1014) = 507000

Least Common Multiple (LCM) of 1000 and 1014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1014. First we will calculate the prime factors of 1000 and 1014.

Prime Factorization of 1000

Prime Factorization of 1014

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1014.

LCM(1000,1014) = 2³ × 5³ × 3¹ × 13²
LCM(1000,1014) = 507000