T=int(input())
from sys import stdin, setrecursionlimit
input = stdin.readline
readline = stdin.readline
import math
for _ in range(T):
  a,b,k=map(int, input().split())
  c=a*b//math.gcd(a,b)
  ok,ng=0,10**20+1
  while (ng-ok)>1:
    mid=(ok+ng)//2
    d=mid-mid//a-mid//b+mid//c
    if d>=k:
      ng=mid 
    else:
      ok=mid 
  print(ng)