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What is the Least Common Multiple of 17311 and 17319?

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 17311 and 17319 is 299809209.

LCM(17311,17319) = 299809209

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Least Common Multiple of 17311 and 17319 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17311 and 17319, than apply into the LCM equation.

GCF(17311,17319) = 1
LCM(17311,17319) = ( 17311 × 17319) / 1
LCM(17311,17319) = 299809209 / 1
LCM(17311,17319) = 299809209

Least Common Multiple (LCM) of 17311 and 17319 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17311 and 17319. First we will calculate the prime factors of 17311 and 17319.

Prime Factorization of 17311

Prime factors of 17311 are 7, 2473. Prime factorization of 17311 in exponential form is:

17311 = 71 × 24731

Prime Factorization of 17319

Prime factors of 17319 are 3, 23, 251. Prime factorization of 17319 in exponential form is:

17319 = 31 × 231 × 2511

Now multiplying the highest exponent prime factors to calculate the LCM of 17311 and 17319.

LCM(17311,17319) = 71 × 24731 × 31 × 231 × 2511
LCM(17311,17319) = 299809209