What is the Least Common Multiple of 17000 and 17017?

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 17017 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 17017, than apply into the LCM equation.

GCF(17000,17017) = 17
LCM(17000,17017) = ( 17000 × 17017) / 17
LCM(17000,17017) = 289289000 / 17
LCM(17000,17017) = 17017000

Least Common Multiple (LCM) of 17000 and 17017 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17000 and 17017. First we will calculate the prime factors of 17000 and 17017.

Prime Factorization of 17000

Prime Factorization of 17017

Now multiplying the highest exponent prime factors to calculate the LCM of 17000 and 17017.

LCM(17000,17017) = 2³ × 5³ × 17¹ × 7¹ × 11¹ × 13¹
LCM(17000,17017) = 17017000