What is the Least Common Multiple of 17000 and 17019?

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 17000 and 17019 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17000 and 17019, than apply into the LCM equation.

GCF(17000,17019) = 1
LCM(17000,17019) = ( 17000 × 17019) / 1
LCM(17000,17019) = 289323000 / 1
LCM(17000,17019) = 289323000

Least Common Multiple (LCM) of 17000 and 17019 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17000 and 17019. First we will calculate the prime factors of 17000 and 17019.

Prime Factorization of 17000

Prime Factorization of 17019

Now multiplying the highest exponent prime factors to calculate the LCM of 17000 and 17019.

LCM(17000,17019) = 2³ × 5³ × 17¹ × 3² × 31¹ × 61¹
LCM(17000,17019) = 289323000