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What is the Least Common Multiple of 13730 and 13750?

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 13750 is 18878750.

LCM(13730,13750) = 18878750

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Least Common Multiple of 13730 and 13750 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 13750, than apply into the LCM equation.

GCF(13730,13750) = 10
LCM(13730,13750) = ( 13730 × 13750) / 10
LCM(13730,13750) = 188787500 / 10
LCM(13730,13750) = 18878750

Least Common Multiple (LCM) of 13730 and 13750 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13730 and 13750. First we will calculate the prime factors of 13730 and 13750.

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 13750

Prime factors of 13750 are 2, 5, 11. Prime factorization of 13750 in exponential form is:

13750 = 21 × 54 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 13730 and 13750.

LCM(13730,13750) = 21 × 54 × 13731 × 111
LCM(13730,13750) = 18878750