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What is the Least Common Multiple of 12312 and 12317?

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 12312 and 12317 is 151646904.

LCM(12312,12317) = 151646904

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Least Common Multiple of 12312 and 12317 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12312 and 12317, than apply into the LCM equation.

GCF(12312,12317) = 1
LCM(12312,12317) = ( 12312 × 12317) / 1
LCM(12312,12317) = 151646904 / 1
LCM(12312,12317) = 151646904

Least Common Multiple (LCM) of 12312 and 12317 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12312 and 12317. First we will calculate the prime factors of 12312 and 12317.

Prime Factorization of 12312

Prime factors of 12312 are 2, 3, 19. Prime factorization of 12312 in exponential form is:

12312 = 23 × 34 × 191

Prime Factorization of 12317

Prime factors of 12317 are 109, 113. Prime factorization of 12317 in exponential form is:

12317 = 1091 × 1131

Now multiplying the highest exponent prime factors to calculate the LCM of 12312 and 12317.

LCM(12312,12317) = 23 × 34 × 191 × 1091 × 1131
LCM(12312,12317) = 151646904