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What is the Least Common Multiple of 13729 and 13746?

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 13729 and 13746 is 188718834.

LCM(13729,13746) = 188718834

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Least Common Multiple of 13729 and 13746 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13729 and 13746, than apply into the LCM equation.

GCF(13729,13746) = 1
LCM(13729,13746) = ( 13729 × 13746) / 1
LCM(13729,13746) = 188718834 / 1
LCM(13729,13746) = 188718834

Least Common Multiple (LCM) of 13729 and 13746 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13729 and 13746. First we will calculate the prime factors of 13729 and 13746.

Prime Factorization of 13729

Prime factors of 13729 are 13729. Prime factorization of 13729 in exponential form is:

13729 = 137291

Prime Factorization of 13746

Prime factors of 13746 are 2, 3, 29, 79. Prime factorization of 13746 in exponential form is:

13746 = 21 × 31 × 291 × 791

Now multiplying the highest exponent prime factors to calculate the LCM of 13729 and 13746.

LCM(13729,13746) = 137291 × 21 × 31 × 291 × 791
LCM(13729,13746) = 188718834