What is the Least Common Multiple of 17000 and 17008?

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 17008 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 17008, than apply into the LCM equation.

GCF(17000,17008) = 8
LCM(17000,17008) = ( 17000 × 17008) / 8
LCM(17000,17008) = 289136000 / 8
LCM(17000,17008) = 36142000

Least Common Multiple (LCM) of 17000 and 17008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17000 and 17008. First we will calculate the prime factors of 17000 and 17008.

Prime Factorization of 17000

Prime Factorization of 17008

Now multiplying the highest exponent prime factors to calculate the LCM of 17000 and 17008.

LCM(17000,17008) = 2⁴ × 5³ × 17¹ × 1063¹
LCM(17000,17008) = 36142000