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What is the Least Common Multiple of 13730 and 13743?

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 13730 and 13743 is 188691390.

LCM(13730,13743) = 188691390

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Least Common Multiple of 13730 and 13743 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13730 and 13743, than apply into the LCM equation.

GCF(13730,13743) = 1
LCM(13730,13743) = ( 13730 × 13743) / 1
LCM(13730,13743) = 188691390 / 1
LCM(13730,13743) = 188691390

Least Common Multiple (LCM) of 13730 and 13743 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13730 and 13743. First we will calculate the prime factors of 13730 and 13743.

Prime Factorization of 13730

Prime factors of 13730 are 2, 5, 1373. Prime factorization of 13730 in exponential form is:

13730 = 21 × 51 × 13731

Prime Factorization of 13743

Prime factors of 13743 are 3, 509. Prime factorization of 13743 in exponential form is:

13743 = 33 × 5091

Now multiplying the highest exponent prime factors to calculate the LCM of 13730 and 13743.

LCM(13730,13743) = 21 × 51 × 13731 × 33 × 5091
LCM(13730,13743) = 188691390