+2653 The sum of the reciprocals of three positive integers is $\frac{13}{12}$. What are the three positive integers?
+1926 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! :)
