What is the Least Common Multiple of 51000 and 51014?

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 51000 and 51014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51000 and 51014, than apply into the LCM equation.

GCF(51000,51014) = 2
LCM(51000,51014) = ( 51000 × 51014) / 2
LCM(51000,51014) = 2601714000 / 2
LCM(51000,51014) = 1300857000

Least Common Multiple (LCM) of 51000 and 51014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51000 and 51014. First we will calculate the prime factors of 51000 and 51014.

Prime Factorization of 51000

Prime Factorization of 51014

Now multiplying the highest exponent prime factors to calculate the LCM of 51000 and 51014.

LCM(51000,51014) = 2³ × 3¹ × 5³ × 17¹ × 23¹ × 1109¹
LCM(51000,51014) = 1300857000