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What is the Least Common Multiple of 13688 and 13699?

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 13688 and 13699 is 187511912.

LCM(13688,13699) = 187511912

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Least Common Multiple of 13688 and 13699 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13688 and 13699, than apply into the LCM equation.

GCF(13688,13699) = 1
LCM(13688,13699) = ( 13688 × 13699) / 1
LCM(13688,13699) = 187511912 / 1
LCM(13688,13699) = 187511912

Least Common Multiple (LCM) of 13688 and 13699 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13688 and 13699. First we will calculate the prime factors of 13688 and 13699.

Prime Factorization of 13688

Prime factors of 13688 are 2, 29, 59. Prime factorization of 13688 in exponential form is:

13688 = 23 × 291 × 591

Prime Factorization of 13699

Prime factors of 13699 are 7, 19, 103. Prime factorization of 13699 in exponential form is:

13699 = 71 × 191 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 13688 and 13699.

LCM(13688,13699) = 23 × 291 × 591 × 71 × 191 × 1031
LCM(13688,13699) = 187511912