If x, y and z are positive integers satisfying 13x=17y=19z, find the minimum value of x+y+z.
I believe that you simply need to find the LCM of the 3 numbers. Since they are all primes, the LCM(13,17,19)=13*17*19=4199.
You then need to find 4199 divided by each of the numbers, giving you the values of x, y, and z. These should be the lowest values. Add them up and you should have your answer.
Let me know if I did anything wrong!