from math import gcd

T = int(input())
for _ in range(T):
  A, B, K = map(int, input().split())
  L = A // gcd(A, B) * B

  ng, ok = 0, 10**19
  while ok - ng > 1:
    md = (ng + ok) // 2
    cnt = md - md//A - md//B + md//L
    if cnt < K: ng = md
    else: ok = md
  print(ok)