What is the Least Common Multiple of 195 and 200?

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 195 and 200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 195 and 200, than apply into the LCM equation.

GCF(195,200) = 5
LCM(195,200) = ( 195 × 200) / 5
LCM(195,200) = 39000 / 5
LCM(195,200) = 7800

Least Common Multiple (LCM) of 195 and 200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 195 and 200. First we will calculate the prime factors of 195 and 200.

Prime Factorization of 195

Prime Factorization of 200

Now multiplying the highest exponent prime factors to calculate the LCM of 195 and 200.

LCM(195,200) = 3¹ × 5² × 13¹ × 2³
LCM(195,200) = 7800