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What is the Least Common Multiple of 17671 and 17689?

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 17671 and 17689 is 312582319.

LCM(17671,17689) = 312582319

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Least Common Multiple of 17671 and 17689 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17671 and 17689, than apply into the LCM equation.

GCF(17671,17689) = 1
LCM(17671,17689) = ( 17671 × 17689) / 1
LCM(17671,17689) = 312582319 / 1
LCM(17671,17689) = 312582319

Least Common Multiple (LCM) of 17671 and 17689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17671 and 17689. First we will calculate the prime factors of 17671 and 17689.

Prime Factorization of 17671

Prime factors of 17671 are 41, 431. Prime factorization of 17671 in exponential form is:

17671 = 411 × 4311

Prime Factorization of 17689

Prime factors of 17689 are 7, 19. Prime factorization of 17689 in exponential form is:

17689 = 72 × 192

Now multiplying the highest exponent prime factors to calculate the LCM of 17671 and 17689.

LCM(17671,17689) = 411 × 4311 × 72 × 192
LCM(17671,17689) = 312582319