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What is the Least Common Multiple of 13698 and 13717?

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 13698 and 13717 is 187895466.

LCM(13698,13717) = 187895466

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Least Common Multiple of 13698 and 13717 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13698 and 13717, than apply into the LCM equation.

GCF(13698,13717) = 1
LCM(13698,13717) = ( 13698 × 13717) / 1
LCM(13698,13717) = 187895466 / 1
LCM(13698,13717) = 187895466

Least Common Multiple (LCM) of 13698 and 13717 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13698 and 13717. First we will calculate the prime factors of 13698 and 13717.

Prime Factorization of 13698

Prime factors of 13698 are 2, 3, 761. Prime factorization of 13698 in exponential form is:

13698 = 21 × 32 × 7611

Prime Factorization of 13717

Prime factors of 13717 are 11, 29, 43. Prime factorization of 13717 in exponential form is:

13717 = 111 × 291 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 13698 and 13717.

LCM(13698,13717) = 21 × 32 × 7611 × 111 × 291 × 431
LCM(13698,13717) = 187895466