Question 702603
You are almost right. The sum is {{{47/60}}}, not {{{47/180}}}.
An extra {{{3}}} factor slipped into your denominator.
Mistakes like that happen to me all the time.
 
Since 3, 4,and 5  are relatively prime to one another (no pair of them has a single common factor),
{{{3*4*5=60=3*20=4*15=5*12}}} is the minimum common multiple and the least common denominator
{{{1/3+1/4+1/5=1*20/(3*20)+1*15/(4*15)+1*12/(5*12)=20/60+15/60+12/60=47/60}}}