#include <bits/stdc++.h> 
using namespace std;
using ll = long long;
#define all(v) v.begin(),v.end()
 #define rep(i,a,b) for(int i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)

ll INF=3e18+100;

long long GCD(long long a, long long b) {
    if (b == 0) return a;
    else return GCD(b, a % b);
}

int main() {
    ios::sync_with_stdio(false);
  cin.tie(0);
  


ll t;cin>>t;
for(ll i=0;i<t;i++) {
  ll A,B,K;cin>>A>>B>>K;

  ll s=1;
  ll g=INF;

  while(s<g) {
    ll k=(s+g)/2;
   ll lcm=A*B/GCD(A,B);
    ll count=k-(k/A)-(k/B)+(k/lcm);
    if(count>=K) g=k;
    else s=k+1;

  }
  


  cout<<s<<'\n';
}

}