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What is the Least Common Multiple of 13585 and 13600?

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 13585 and 13600 is 36951200.

LCM(13585,13600) = 36951200

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Least Common Multiple of 13585 and 13600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13585 and 13600, than apply into the LCM equation.

GCF(13585,13600) = 5
LCM(13585,13600) = ( 13585 × 13600) / 5
LCM(13585,13600) = 184756000 / 5
LCM(13585,13600) = 36951200

Least Common Multiple (LCM) of 13585 and 13600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13585 and 13600. First we will calculate the prime factors of 13585 and 13600.

Prime Factorization of 13585

Prime factors of 13585 are 5, 11, 13, 19. Prime factorization of 13585 in exponential form is:

13585 = 51 × 111 × 131 × 191

Prime Factorization of 13600

Prime factors of 13600 are 2, 5, 17. Prime factorization of 13600 in exponential form is:

13600 = 25 × 52 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 13585 and 13600.

LCM(13585,13600) = 52 × 111 × 131 × 191 × 25 × 171
LCM(13585,13600) = 36951200