# Least Common Multiple of 200 and 205

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 (LCM) of 200 and 205 is 8200.

LCM(200,205) = 8200

LCM Calculator and

## Least Common Multiple of 200 and 205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 200 and 205, than apply into the LCM equation.

GCF(200,205) = 5
LCM(200,205) = ( 200 × 205) / 5
LCM(200,205) = 41000 / 5
LCM(200,205) = 8200

## Least Common Multiple (LCM) of 200 and 205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 200 and 205. First we will calculate the prime factors of 200 and 205.

### Prime Factorization of 200

Prime factors of 200 are 2, 5. Prime factorization of 200 in exponential form is:

200 = 23 × 52

### Prime Factorization of 205

Prime factors of 205 are 5, 41. Prime factorization of 205 in exponential form is:

205 = 51 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 200 and 205.

LCM(200,205) = 23 × 52 × 411
LCM(200,205) = 8200