What is the Least Common Multiple of 17500 and 17514?

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 17500 and 17514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17500 and 17514, than apply into the LCM equation.

GCF(17500,17514) = 14
LCM(17500,17514) = ( 17500 × 17514) / 14
LCM(17500,17514) = 306495000 / 14
LCM(17500,17514) = 21892500

Least Common Multiple (LCM) of 17500 and 17514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17500 and 17514. First we will calculate the prime factors of 17500 and 17514.

Prime Factorization of 17500

Prime Factorization of 17514

Now multiplying the highest exponent prime factors to calculate the LCM of 17500 and 17514.

LCM(17500,17514) = 2² × 5⁴ × 7¹ × 3² × 139¹
LCM(17500,17514) = 21892500