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What is the Least Common Multiple of 16704 and 16723?

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 16704 and 16723 is 279340992.

LCM(16704,16723) = 279340992

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Least Common Multiple of 16704 and 16723 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16704 and 16723, than apply into the LCM equation.

GCF(16704,16723) = 1
LCM(16704,16723) = ( 16704 × 16723) / 1
LCM(16704,16723) = 279340992 / 1
LCM(16704,16723) = 279340992

Least Common Multiple (LCM) of 16704 and 16723 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16704 and 16723. First we will calculate the prime factors of 16704 and 16723.

Prime Factorization of 16704

Prime factors of 16704 are 2, 3, 29. Prime factorization of 16704 in exponential form is:

16704 = 26 × 32 × 291

Prime Factorization of 16723

Prime factors of 16723 are 7, 2389. Prime factorization of 16723 in exponential form is:

16723 = 71 × 23891

Now multiplying the highest exponent prime factors to calculate the LCM of 16704 and 16723.

LCM(16704,16723) = 26 × 32 × 291 × 71 × 23891
LCM(16704,16723) = 279340992