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What is the Least Common Multiple of 17705 and 17724?

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 17705 and 17724 is 313803420.

LCM(17705,17724) = 313803420

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Least Common Multiple of 17705 and 17724 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17705 and 17724, than apply into the LCM equation.

GCF(17705,17724) = 1
LCM(17705,17724) = ( 17705 × 17724) / 1
LCM(17705,17724) = 313803420 / 1
LCM(17705,17724) = 313803420

Least Common Multiple (LCM) of 17705 and 17724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17705 and 17724. First we will calculate the prime factors of 17705 and 17724.

Prime Factorization of 17705

Prime factors of 17705 are 5, 3541. Prime factorization of 17705 in exponential form is:

17705 = 51 × 35411

Prime Factorization of 17724

Prime factors of 17724 are 2, 3, 7, 211. Prime factorization of 17724 in exponential form is:

17724 = 22 × 31 × 71 × 2111

Now multiplying the highest exponent prime factors to calculate the LCM of 17705 and 17724.

LCM(17705,17724) = 51 × 35411 × 22 × 31 × 71 × 2111
LCM(17705,17724) = 313803420