If (x+y) : (y+z) : (x+z) = 10 : 23 : 19 and x + y + z = 13, then the value of z?

Question

x, y, z and k are four non zero positive integers satisfying 1/x + y/2 = z/3 + 4/k, minimum integral value of k for integral value of x, y and z will be