Number Theory

Fill in the blanks with three distinct positive integers.    
1/___ + 1/___ + 1/___ = \frac{13}{12}    

I answered this once before and my answer was good,

but then I saw a better answer.  Here's the better answer.    

1/2  +  1/3  +  1/4    

6/12 + 4/12 + 3/12  =  13/12    

_.    

13/12 =  1/1  + 1/12  =  1/1  + 1/13 + 1/156

The first fraction is  easy....use the "Egyptian Method" to  generate the last two....this will give us fractions with numerators  =1

Second fraction  denominator = invert the second fraction  and  add 1   =  12/1 + 1 =  13

Second fraction =1/13

Subtract  1/12 -1/13  to get the last fraction

112 -1/13  = [ 13 -12] / 156   =1/156