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What is the Least Common Multiple of 17106 and 17112?

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 17106 and 17112 is 48786312.

LCM(17106,17112) = 48786312

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Least Common Multiple of 17106 and 17112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17106 and 17112, than apply into the LCM equation.

GCF(17106,17112) = 6
LCM(17106,17112) = ( 17106 × 17112) / 6
LCM(17106,17112) = 292717872 / 6
LCM(17106,17112) = 48786312

Least Common Multiple (LCM) of 17106 and 17112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17106 and 17112. First we will calculate the prime factors of 17106 and 17112.

Prime Factorization of 17106

Prime factors of 17106 are 2, 3, 2851. Prime factorization of 17106 in exponential form is:

17106 = 21 × 31 × 28511

Prime Factorization of 17112

Prime factors of 17112 are 2, 3, 23, 31. Prime factorization of 17112 in exponential form is:

17112 = 23 × 31 × 231 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 17106 and 17112.

LCM(17106,17112) = 23 × 31 × 28511 × 231 × 311
LCM(17106,17112) = 48786312