Question

If a and b are coprime positive integers such that

1/2+1/3+1/4+1/5=ab,
what is the value of a+b?

Answer 1

Naturally, a sum of a few small fractions cannot be the product of two integers, each greater than 1.

Now, if you meant a/b, then

1/2 + 1/3 + 1/4 + 1/5 = 77/60

a+b = 137