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What is the Least Common Multiple of 17268 and 17280?

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 17268 and 17280 is 24865920.

LCM(17268,17280) = 24865920

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Least Common Multiple of 17268 and 17280 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17268 and 17280, than apply into the LCM equation.

GCF(17268,17280) = 12
LCM(17268,17280) = ( 17268 × 17280) / 12
LCM(17268,17280) = 298391040 / 12
LCM(17268,17280) = 24865920

Least Common Multiple (LCM) of 17268 and 17280 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17268 and 17280. First we will calculate the prime factors of 17268 and 17280.

Prime Factorization of 17268

Prime factors of 17268 are 2, 3, 1439. Prime factorization of 17268 in exponential form is:

17268 = 22 × 31 × 14391

Prime Factorization of 17280

Prime factors of 17280 are 2, 3, 5. Prime factorization of 17280 in exponential form is:

17280 = 27 × 33 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 17268 and 17280.

LCM(17268,17280) = 27 × 33 × 14391 × 51
LCM(17268,17280) = 24865920