What is the Least Common Multiple of 20500 and 20517?

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 20500 and 20517 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20500 and 20517, than apply into the LCM equation.

GCF(20500,20517) = 1
LCM(20500,20517) = ( 20500 × 20517) / 1
LCM(20500,20517) = 420598500 / 1
LCM(20500,20517) = 420598500

Least Common Multiple (LCM) of 20500 and 20517 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20500 and 20517. First we will calculate the prime factors of 20500 and 20517.

Prime Factorization of 20500

Prime Factorization of 20517

Now multiplying the highest exponent prime factors to calculate the LCM of 20500 and 20517.

LCM(20500,20517) = 2² × 5³ × 41¹ × 3¹ × 7¹ × 977¹
LCM(20500,20517) = 420598500