from math import lcm

def is_ok(md):
  cnt = md - md//A - md//B + md//L
  return cnt >= K

for _ in range(T := int(input())):
  A, B, K = map(int, input().split())
  L = lcm(A, B)
  
  ng, ok = 0, 10**19
  while abs(ok - ng) > 1:
    md = (ng + ok) // 2
    if is_ok(md): ok = md
    else: ng = md
  
  print(ok)