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What is the Least Common Multiple of 17589 and 17598?

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 17589 and 17598 is 103177074.

LCM(17589,17598) = 103177074

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Least Common Multiple of 17589 and 17598 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17589 and 17598, than apply into the LCM equation.

GCF(17589,17598) = 3
LCM(17589,17598) = ( 17589 × 17598) / 3
LCM(17589,17598) = 309531222 / 3
LCM(17589,17598) = 103177074

Least Common Multiple (LCM) of 17589 and 17598 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17589 and 17598. First we will calculate the prime factors of 17589 and 17598.

Prime Factorization of 17589

Prime factors of 17589 are 3, 11, 13, 41. Prime factorization of 17589 in exponential form is:

17589 = 31 × 111 × 131 × 411

Prime Factorization of 17598

Prime factors of 17598 are 2, 3, 7, 419. Prime factorization of 17598 in exponential form is:

17598 = 21 × 31 × 71 × 4191

Now multiplying the highest exponent prime factors to calculate the LCM of 17589 and 17598.

LCM(17589,17598) = 31 × 111 × 131 × 411 × 21 × 71 × 4191
LCM(17589,17598) = 103177074