What is the Least Common Multiple of 10208 and 10214?

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 10208 and 10214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10208 and 10214, than apply into the LCM equation.

GCF(10208,10214) = 2
LCM(10208,10214) = ( 10208 × 10214) / 2
LCM(10208,10214) = 104264512 / 2
LCM(10208,10214) = 52132256

Least Common Multiple (LCM) of 10208 and 10214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10208 and 10214. First we will calculate the prime factors of 10208 and 10214.

Prime Factorization of 10208

Prime Factorization of 10214

Now multiplying the highest exponent prime factors to calculate the LCM of 10208 and 10214.

LCM(10208,10214) = 2⁵ × 11¹ × 29¹ × 5107¹
LCM(10208,10214) = 52132256