Question 1048379
{{{1/x+1/y = 1/12}}}

<===> {{{y=(12x)/(x-12)}}} <===> {{{y=12(1+12/(x-12))}}}.

Since x and y are positive integers, x-12 must divide 12.

===> x-12 = 1,2,3,4,6,12

Obviously, the value of x-12 that would maximize y is 1, which would give x = 13. The corresponding value of y would be 156.