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What is the Least Common Multiple of 17512 and 17521?

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 17512 and 17521 is 306827752.

LCM(17512,17521) = 306827752

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Least Common Multiple of 17512 and 17521 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17512 and 17521, than apply into the LCM equation.

GCF(17512,17521) = 1
LCM(17512,17521) = ( 17512 × 17521) / 1
LCM(17512,17521) = 306827752 / 1
LCM(17512,17521) = 306827752

Least Common Multiple (LCM) of 17512 and 17521 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17512 and 17521. First we will calculate the prime factors of 17512 and 17521.

Prime Factorization of 17512

Prime factors of 17512 are 2, 11, 199. Prime factorization of 17512 in exponential form is:

17512 = 23 × 111 × 1991

Prime Factorization of 17521

Prime factors of 17521 are 7, 2503. Prime factorization of 17521 in exponential form is:

17521 = 71 × 25031

Now multiplying the highest exponent prime factors to calculate the LCM of 17512 and 17521.

LCM(17512,17521) = 23 × 111 × 1991 × 71 × 25031
LCM(17512,17521) = 306827752