Question 276506
Let A,B,and C be the integers.
Since they are positive, then the minimum A could be is,
{{{A=1}}}
Since they are different, then the minimum B could be is, 
{{{B=2}}}
Then from the average,
{{{(A+B+C)/3=60}}} or
{{{A+B+C=180}}}
Substituting,
{{{1+2+C=180}}}
{{{C=177}}}
The greatest value for one of the integers would be 177.