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What is the Least Common Multiple of 16688 and 16704?

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 16688 and 16704 is 17422272.

LCM(16688,16704) = 17422272

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Least Common Multiple of 16688 and 16704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16688 and 16704, than apply into the LCM equation.

GCF(16688,16704) = 16
LCM(16688,16704) = ( 16688 × 16704) / 16
LCM(16688,16704) = 278756352 / 16
LCM(16688,16704) = 17422272

Least Common Multiple (LCM) of 16688 and 16704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16688 and 16704. First we will calculate the prime factors of 16688 and 16704.

Prime Factorization of 16688

Prime factors of 16688 are 2, 7, 149. Prime factorization of 16688 in exponential form is:

16688 = 24 × 71 × 1491

Prime Factorization of 16704

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

16704 = 26 × 32 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 16688 and 16704.

LCM(16688,16704) = 26 × 71 × 1491 × 32 × 291
LCM(16688,16704) = 17422272