from math import*
t=int(input())
for _ in range(t):
  a,b,k=map(int,input().split())
  l=a*b//gcd(a,b)
  ok,ng=10**20,0
  while abs(ok-ng)>1:
    mid=ok+ng>>1
    if k<=mid+mid//l-mid//a-mid//b:
      ok=mid
    else:
      ng=mid
  print(ok)