from math import gcd

def is_ok(md):
	cnt = md - md//A - md//B + md//L
	return cnt >= K
def bis(ok, ng):
  while abs(ok - ng) > 1:
    md = (ng + ok) // 2
    if is_ok(md): ok = md
    else: ng = md
  return ok

T = int(input())
for _ in range(T):
  A, B, K = map(int, input().split())
  L = A // gcd(A, B) * B
  print(bis(10**19, 0))