t=int(input())
import math
for _ in range(t):
  a,b,k=map(int,input().split())
  g=math.gcd(a,b)
  ok=0
  ng=10**30
  while abs(ok-ng)>1:
    m=(ok+ng)//2
    if m-(m//a+m//b-m//((a*b)//g))<=k:
      ok=m
    else:
      ng=m
  print(ok)