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What is the Least Common Multiple of 17717 and 17728?

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 17717 and 17728 is 314086976.

LCM(17717,17728) = 314086976

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Least Common Multiple of 17717 and 17728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17717 and 17728, than apply into the LCM equation.

GCF(17717,17728) = 1
LCM(17717,17728) = ( 17717 × 17728) / 1
LCM(17717,17728) = 314086976 / 1
LCM(17717,17728) = 314086976

Least Common Multiple (LCM) of 17717 and 17728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17717 and 17728. First we will calculate the prime factors of 17717 and 17728.

Prime Factorization of 17717

Prime factors of 17717 are 7, 2531. Prime factorization of 17717 in exponential form is:

17717 = 71 × 25311

Prime Factorization of 17728

Prime factors of 17728 are 2, 277. Prime factorization of 17728 in exponential form is:

17728 = 26 × 2771

Now multiplying the highest exponent prime factors to calculate the LCM of 17717 and 17728.

LCM(17717,17728) = 71 × 25311 × 26 × 2771
LCM(17717,17728) = 314086976