import math

t = int(input())
  
def f(a, b, k, x):
  sum = 0

  sum += x // a
  sum += x // b
  sum -= x // math.lcm(a, b)

  return (x - sum >= k)

for _ in range(t):
  a, b, k = map(int, input().split())

  l = 0
  r = int(5e18)
  while r - l > 1:
    m = (l + r) // 2
    if f(a, b, k, m):
      r = m
    else:
      l = m
  
  print(r)