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What is the Least Common Multiple of 13686 and 13700?

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 13686 and 13700 is 93749100.

LCM(13686,13700) = 93749100

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Least Common Multiple of 13686 and 13700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13686 and 13700, than apply into the LCM equation.

GCF(13686,13700) = 2
LCM(13686,13700) = ( 13686 × 13700) / 2
LCM(13686,13700) = 187498200 / 2
LCM(13686,13700) = 93749100

Least Common Multiple (LCM) of 13686 and 13700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13686 and 13700. First we will calculate the prime factors of 13686 and 13700.

Prime Factorization of 13686

Prime factors of 13686 are 2, 3, 2281. Prime factorization of 13686 in exponential form is:

13686 = 21 × 31 × 22811

Prime Factorization of 13700

Prime factors of 13700 are 2, 5, 137. Prime factorization of 13700 in exponential form is:

13700 = 22 × 52 × 1371

Now multiplying the highest exponent prime factors to calculate the LCM of 13686 and 13700.

LCM(13686,13700) = 22 × 31 × 22811 × 52 × 1371
LCM(13686,13700) = 93749100