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What is the Least Common Multiple of 13857 and 13864?

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 13857 and 13864 is 192113448.

LCM(13857,13864) = 192113448

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Least Common Multiple of 13857 and 13864 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13857 and 13864, than apply into the LCM equation.

GCF(13857,13864) = 1
LCM(13857,13864) = ( 13857 × 13864) / 1
LCM(13857,13864) = 192113448 / 1
LCM(13857,13864) = 192113448

Least Common Multiple (LCM) of 13857 and 13864 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13857 and 13864. First we will calculate the prime factors of 13857 and 13864.

Prime Factorization of 13857

Prime factors of 13857 are 3, 31, 149. Prime factorization of 13857 in exponential form is:

13857 = 31 × 311 × 1491

Prime Factorization of 13864

Prime factors of 13864 are 2, 1733. Prime factorization of 13864 in exponential form is:

13864 = 23 × 17331

Now multiplying the highest exponent prime factors to calculate the LCM of 13857 and 13864.

LCM(13857,13864) = 31 × 311 × 1491 × 23 × 17331
LCM(13857,13864) = 192113448