What is the Least Common Multiple of 10198 and 10208?

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 10198 and 10208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10198 and 10208, than apply into the LCM equation.

GCF(10198,10208) = 2
LCM(10198,10208) = ( 10198 × 10208) / 2
LCM(10198,10208) = 104101184 / 2
LCM(10198,10208) = 52050592

Least Common Multiple (LCM) of 10198 and 10208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10198 and 10208. First we will calculate the prime factors of 10198 and 10208.

Prime Factorization of 10198

Prime Factorization of 10208

Now multiplying the highest exponent prime factors to calculate the LCM of 10198 and 10208.

LCM(10198,10208) = 2⁵ × 5099¹ × 11¹ × 29¹
LCM(10198,10208) = 52050592