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What is the Least Common Multiple of 10208 and 10213?

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 10208 and 10213 is 104254304.

LCM(10208,10213) = 104254304

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Least Common Multiple of 10208 and 10213 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 10213, than apply into the LCM equation.

GCF(10208,10213) = 1
LCM(10208,10213) = ( 10208 × 10213) / 1
LCM(10208,10213) = 104254304 / 1
LCM(10208,10213) = 104254304

Least Common Multiple (LCM) of 10208 and 10213 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10208 and 10213. First we will calculate the prime factors of 10208 and 10213.

Prime Factorization of 10208

Prime factors of 10208 are 2, 11, 29. Prime factorization of 10208 in exponential form is:

10208 = 25 × 111 × 291

Prime Factorization of 10213

Prime factors of 10213 are 7, 1459. Prime factorization of 10213 in exponential form is:

10213 = 71 × 14591

Now multiplying the highest exponent prime factors to calculate the LCM of 10208 and 10213.

LCM(10208,10213) = 25 × 111 × 291 × 71 × 14591
LCM(10208,10213) = 104254304