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What is the Least Common Multiple of 13728 and 13739?

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 13728 and 13739 is 17146272.

LCM(13728,13739) = 17146272

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Least Common Multiple of 13728 and 13739 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13728 and 13739, than apply into the LCM equation.

GCF(13728,13739) = 11
LCM(13728,13739) = ( 13728 × 13739) / 11
LCM(13728,13739) = 188608992 / 11
LCM(13728,13739) = 17146272

Least Common Multiple (LCM) of 13728 and 13739 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13728 and 13739. First we will calculate the prime factors of 13728 and 13739.

Prime Factorization of 13728

Prime factors of 13728 are 2, 3, 11, 13. Prime factorization of 13728 in exponential form is:

13728 = 25 × 31 × 111 × 131

Prime Factorization of 13739

Prime factors of 13739 are 11, 1249. Prime factorization of 13739 in exponential form is:

13739 = 111 × 12491

Now multiplying the highest exponent prime factors to calculate the LCM of 13728 and 13739.

LCM(13728,13739) = 25 × 31 × 111 × 131 × 12491
LCM(13728,13739) = 17146272