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What is the Least Common Multiple of 13870 and 13889?

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 13870 and 13889 is 10138970.

LCM(13870,13889) = 10138970

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Least Common Multiple of 13870 and 13889 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13870 and 13889, than apply into the LCM equation.

GCF(13870,13889) = 19
LCM(13870,13889) = ( 13870 × 13889) / 19
LCM(13870,13889) = 192640430 / 19
LCM(13870,13889) = 10138970

Least Common Multiple (LCM) of 13870 and 13889 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13870 and 13889. First we will calculate the prime factors of 13870 and 13889.

Prime Factorization of 13870

Prime factors of 13870 are 2, 5, 19, 73. Prime factorization of 13870 in exponential form is:

13870 = 21 × 51 × 191 × 731

Prime Factorization of 13889

Prime factors of 13889 are 17, 19, 43. Prime factorization of 13889 in exponential form is:

13889 = 171 × 191 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 13870 and 13889.

LCM(13870,13889) = 21 × 51 × 191 × 731 × 171 × 431
LCM(13870,13889) = 10138970