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What is the Least Common Multiple of 13719 and 13730?

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 13719 and 13730 is 188361870.

LCM(13719,13730) = 188361870

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Least Common Multiple of 13719 and 13730 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13719 and 13730, than apply into the LCM equation.

GCF(13719,13730) = 1
LCM(13719,13730) = ( 13719 × 13730) / 1
LCM(13719,13730) = 188361870 / 1
LCM(13719,13730) = 188361870

Least Common Multiple (LCM) of 13719 and 13730 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13719 and 13730. First we will calculate the prime factors of 13719 and 13730.

Prime Factorization of 13719

Prime factors of 13719 are 3, 17, 269. Prime factorization of 13719 in exponential form is:

13719 = 31 × 171 × 2691

Prime Factorization of 13730

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

13730 = 21 × 51 × 13731

Now multiplying the highest exponent prime factors to calculate the LCM of 13719 and 13730.

LCM(13719,13730) = 31 × 171 × 2691 × 21 × 51 × 13731
LCM(13719,13730) = 188361870