What is the Least Common Multiple of 10085 and 10100?

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 10085 and 10100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10085 and 10100, than apply into the LCM equation.

GCF(10085,10100) = 5
LCM(10085,10100) = ( 10085 × 10100) / 5
LCM(10085,10100) = 101858500 / 5
LCM(10085,10100) = 20371700

Least Common Multiple (LCM) of 10085 and 10100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10085 and 10100. First we will calculate the prime factors of 10085 and 10100.

Prime Factorization of 10085

Prime Factorization of 10100

Now multiplying the highest exponent prime factors to calculate the LCM of 10085 and 10100.

LCM(10085,10100) = 5² × 2017¹ × 2² × 101¹
LCM(10085,10100) = 20371700