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What is the Least Common Multiple of 13585 and 13598?

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 13598 is 14209910.

LCM(13585,13598) = 14209910

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Least Common Multiple of 13585 and 13598 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 13598, than apply into the LCM equation.

GCF(13585,13598) = 13
LCM(13585,13598) = ( 13585 × 13598) / 13
LCM(13585,13598) = 184728830 / 13
LCM(13585,13598) = 14209910

Least Common Multiple (LCM) of 13585 and 13598 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13585 and 13598. First we will calculate the prime factors of 13585 and 13598.

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 13598

Prime factors of 13598 are 2, 13, 523. Prime factorization of 13598 in exponential form is:

13598 = 21 × 131 × 5231

Now multiplying the highest exponent prime factors to calculate the LCM of 13585 and 13598.

LCM(13585,13598) = 51 × 111 × 131 × 191 × 21 × 5231
LCM(13585,13598) = 14209910