What is the Least Common Multiple of 8500 and 8505?

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 8500 and 8505 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8500 and 8505, than apply into the LCM equation.

GCF(8500,8505) = 5
LCM(8500,8505) = ( 8500 × 8505) / 5
LCM(8500,8505) = 72292500 / 5
LCM(8500,8505) = 14458500

Least Common Multiple (LCM) of 8500 and 8505 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8500 and 8505. First we will calculate the prime factors of 8500 and 8505.

Prime Factorization of 8500

Prime Factorization of 8505

Now multiplying the highest exponent prime factors to calculate the LCM of 8500 and 8505.

LCM(8500,8505) = 2² × 5³ × 17¹ × 3⁵ × 7¹
LCM(8500,8505) = 14458500