What is the Least Common Multiple of 17085 and 17100?

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 17085 and 17100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17085 and 17100, than apply into the LCM equation.

GCF(17085,17100) = 15
LCM(17085,17100) = ( 17085 × 17100) / 15
LCM(17085,17100) = 292153500 / 15
LCM(17085,17100) = 19476900

Least Common Multiple (LCM) of 17085 and 17100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17085 and 17100. First we will calculate the prime factors of 17085 and 17100.

Prime Factorization of 17085

Prime Factorization of 17100

Now multiplying the highest exponent prime factors to calculate the LCM of 17085 and 17100.

LCM(17085,17100) = 3² × 5² × 17¹ × 67¹ × 2² × 19¹
LCM(17085,17100) = 19476900