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What is the Least Common Multiple of 17296 and 17306?

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 17296 and 17306 is 149662288.

LCM(17296,17306) = 149662288

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Least Common Multiple of 17296 and 17306 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17296 and 17306, than apply into the LCM equation.

GCF(17296,17306) = 2
LCM(17296,17306) = ( 17296 × 17306) / 2
LCM(17296,17306) = 299324576 / 2
LCM(17296,17306) = 149662288

Least Common Multiple (LCM) of 17296 and 17306 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17296 and 17306. First we will calculate the prime factors of 17296 and 17306.

Prime Factorization of 17296

Prime factors of 17296 are 2, 23, 47. Prime factorization of 17296 in exponential form is:

17296 = 24 × 231 × 471

Prime Factorization of 17306

Prime factors of 17306 are 2, 17, 509. Prime factorization of 17306 in exponential form is:

17306 = 21 × 171 × 5091

Now multiplying the highest exponent prime factors to calculate the LCM of 17296 and 17306.

LCM(17296,17306) = 24 × 231 × 471 × 171 × 5091
LCM(17296,17306) = 149662288