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What is the Least Common Multiple of 17580 and 17592?

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 17580 and 17592 is 25772280.

LCM(17580,17592) = 25772280

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Least Common Multiple of 17580 and 17592 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17580 and 17592, than apply into the LCM equation.

GCF(17580,17592) = 12
LCM(17580,17592) = ( 17580 × 17592) / 12
LCM(17580,17592) = 309267360 / 12
LCM(17580,17592) = 25772280

Least Common Multiple (LCM) of 17580 and 17592 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17580 and 17592. First we will calculate the prime factors of 17580 and 17592.

Prime Factorization of 17580

Prime factors of 17580 are 2, 3, 5, 293. Prime factorization of 17580 in exponential form is:

17580 = 22 × 31 × 51 × 2931

Prime Factorization of 17592

Prime factors of 17592 are 2, 3, 733. Prime factorization of 17592 in exponential form is:

17592 = 23 × 31 × 7331

Now multiplying the highest exponent prime factors to calculate the LCM of 17580 and 17592.

LCM(17580,17592) = 23 × 31 × 51 × 2931 × 7331
LCM(17580,17592) = 25772280