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What is the Least Common Multiple of 13685 and 13704?

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 13685 and 13704 is 187539240.

LCM(13685,13704) = 187539240

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Least Common Multiple of 13685 and 13704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13685 and 13704, than apply into the LCM equation.

GCF(13685,13704) = 1
LCM(13685,13704) = ( 13685 × 13704) / 1
LCM(13685,13704) = 187539240 / 1
LCM(13685,13704) = 187539240

Least Common Multiple (LCM) of 13685 and 13704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13685 and 13704. First we will calculate the prime factors of 13685 and 13704.

Prime Factorization of 13685

Prime factors of 13685 are 5, 7, 17, 23. Prime factorization of 13685 in exponential form is:

13685 = 51 × 71 × 171 × 231

Prime Factorization of 13704

Prime factors of 13704 are 2, 3, 571. Prime factorization of 13704 in exponential form is:

13704 = 23 × 31 × 5711

Now multiplying the highest exponent prime factors to calculate the LCM of 13685 and 13704.

LCM(13685,13704) = 51 × 71 × 171 × 231 × 23 × 31 × 5711
LCM(13685,13704) = 187539240