What is the Least Common Multiple of 17460 and 17475?

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 17460 and 17475 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17460 and 17475, than apply into the LCM equation.

GCF(17460,17475) = 15
LCM(17460,17475) = ( 17460 × 17475) / 15
LCM(17460,17475) = 305113500 / 15
LCM(17460,17475) = 20340900

Least Common Multiple (LCM) of 17460 and 17475 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17460 and 17475. First we will calculate the prime factors of 17460 and 17475.

Prime Factorization of 17460

Prime Factorization of 17475

Now multiplying the highest exponent prime factors to calculate the LCM of 17460 and 17475.

LCM(17460,17475) = 2² × 3² × 5² × 97¹ × 233¹
LCM(17460,17475) = 20340900