Given a number k you have to write it as a sum of numbers equal to k such that the lcm of the chosen numbers is maximum. eg. Given 12 write it as 5+4+3=12 because lcm(3,4,5) = 60.It can be verified that 60 is the best that can be done.

What would be the best strategy for solving this problem. My guess is that I should only be considering the cases where the number can be expressed as the sum of relatively prime numbers?