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What is the Least Common Multiple of 10396 and 10415?

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 10396 and 10415 is 108274340.

LCM(10396,10415) = 108274340

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Least Common Multiple of 10396 and 10415 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10396 and 10415, than apply into the LCM equation.

GCF(10396,10415) = 1
LCM(10396,10415) = ( 10396 × 10415) / 1
LCM(10396,10415) = 108274340 / 1
LCM(10396,10415) = 108274340

Least Common Multiple (LCM) of 10396 and 10415 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10396 and 10415. First we will calculate the prime factors of 10396 and 10415.

Prime Factorization of 10396

Prime factors of 10396 are 2, 23, 113. Prime factorization of 10396 in exponential form is:

10396 = 22 × 231 × 1131

Prime Factorization of 10415

Prime factors of 10415 are 5, 2083. Prime factorization of 10415 in exponential form is:

10415 = 51 × 20831

Now multiplying the highest exponent prime factors to calculate the LCM of 10396 and 10415.

LCM(10396,10415) = 22 × 231 × 1131 × 51 × 20831
LCM(10396,10415) = 108274340