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What is the Least Common Multiple of 17709 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 17709 and 17728 is 313945152.

LCM(17709,17728) = 313945152

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Least Common Multiple of 17709 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 17709 and 17728, than apply into the LCM equation.

GCF(17709,17728) = 1
LCM(17709,17728) = ( 17709 × 17728) / 1
LCM(17709,17728) = 313945152 / 1
LCM(17709,17728) = 313945152

Least Common Multiple (LCM) of 17709 and 17728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17709 and 17728. First we will calculate the prime factors of 17709 and 17728.

Prime Factorization of 17709

Prime factors of 17709 are 3, 5903. Prime factorization of 17709 in exponential form is:

17709 = 31 × 59031

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 17709 and 17728.

LCM(17709,17728) = 31 × 59031 × 26 × 2771
LCM(17709,17728) = 313945152