#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(v) v.begin(),v.end()
typedef long long ll;
 
#include<bits/stdc++.h>
using namespace std;

int main(){
  ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  
  int t;
  cin>>t;
  while(t--){
    ll a,b,k;
    cin>>a>>b>>k;
    ll c=lcm(a,b);
    
    auto f=[&](ll x){
      return x-x/a-x/b+x/c;
    };
    
    ll ok=8e18+1,ng=0;
    while(ok-ng>1){
      ll mid=(ok+ng)/2;
      if(f(mid)>=k) ok=mid;
      else ng=mid;
    }
    cout<<ok<<endl;
  }
  
  return 0;
}