Number Theory

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! :)