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What is the Least Common Multiple of 8512 and 8517?

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 8512 and 8517 is 72496704.

LCM(8512,8517) = 72496704

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Least Common Multiple of 8512 and 8517 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8512 and 8517, than apply into the LCM equation.

GCF(8512,8517) = 1
LCM(8512,8517) = ( 8512 × 8517) / 1
LCM(8512,8517) = 72496704 / 1
LCM(8512,8517) = 72496704

Least Common Multiple (LCM) of 8512 and 8517 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8512 and 8517. First we will calculate the prime factors of 8512 and 8517.

Prime Factorization of 8512

Prime factors of 8512 are 2, 7, 19. Prime factorization of 8512 in exponential form is:

8512 = 26 × 71 × 191

Prime Factorization of 8517

Prime factors of 8517 are 3, 17, 167. Prime factorization of 8517 in exponential form is:

8517 = 31 × 171 × 1671

Now multiplying the highest exponent prime factors to calculate the LCM of 8512 and 8517.

LCM(8512,8517) = 26 × 71 × 191 × 31 × 171 × 1671
LCM(8512,8517) = 72496704