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What is the Least Common Multiple of 17313 and 17317?

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 17313 and 17317 is 299809221.

LCM(17313,17317) = 299809221

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Least Common Multiple of 17313 and 17317 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17313 and 17317, than apply into the LCM equation.

GCF(17313,17317) = 1
LCM(17313,17317) = ( 17313 × 17317) / 1
LCM(17313,17317) = 299809221 / 1
LCM(17313,17317) = 299809221

Least Common Multiple (LCM) of 17313 and 17317 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17313 and 17317. First we will calculate the prime factors of 17313 and 17317.

Prime Factorization of 17313

Prime factors of 17313 are 3, 29, 199. Prime factorization of 17313 in exponential form is:

17313 = 31 × 291 × 1991

Prime Factorization of 17317

Prime factors of 17317 are 17317. Prime factorization of 17317 in exponential form is:

17317 = 173171

Now multiplying the highest exponent prime factors to calculate the LCM of 17313 and 17317.

LCM(17313,17317) = 31 × 291 × 1991 × 173171
LCM(17313,17317) = 299809221