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The sum of the reciprocals of three positive integers is $\frac{13}{12}$.  What are the three positive integers?

 Jun 20, 2024
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We want to try to find 3 numbers with an Least Common Multiple of 12.

We also want these integers to be as small as possible, but can't let it be 1.  

 

Let's take a look at the numbers \(2, 3,4\)

 

The reciprocals of these numbers are

\(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\)

 

Let's add these fractions up. We get

\(\frac{1}{2}+ \frac{1}{3}+ \frac{1}{4}\)

 

The common denominator is 12. Converting all fractions to a denominator of 12, we get

\(\frac{6}{12}+ \frac{4}{12}+ \frac{3}{12} = \frac{13}{12}\)

 

So 2,3 and 4 are our answers. 

 

Thanks! :)

 Jun 20, 2024
edited by NotThatSmart  Jun 20, 2024

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