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What is the Least Common Multiple of 17576 and 17585?

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 17576 and 17585 is 309073960.

LCM(17576,17585) = 309073960

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Least Common Multiple of 17576 and 17585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17576 and 17585, than apply into the LCM equation.

GCF(17576,17585) = 1
LCM(17576,17585) = ( 17576 × 17585) / 1
LCM(17576,17585) = 309073960 / 1
LCM(17576,17585) = 309073960

Least Common Multiple (LCM) of 17576 and 17585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17576 and 17585. First we will calculate the prime factors of 17576 and 17585.

Prime Factorization of 17576

Prime factors of 17576 are 2, 13. Prime factorization of 17576 in exponential form is:

17576 = 23 × 133

Prime Factorization of 17585

Prime factors of 17585 are 5, 3517. Prime factorization of 17585 in exponential form is:

17585 = 51 × 35171

Now multiplying the highest exponent prime factors to calculate the LCM of 17576 and 17585.

LCM(17576,17585) = 23 × 133 × 51 × 35171
LCM(17576,17585) = 309073960