#include<bits/stdc++.h>
using namespace std;
using ll=long long;
#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
template<class T> bool chmax(T &a, T b){if (a < b){a = b;return true;} else return false;}
template<class T> bool chmin(T &a, T b){if (a > b){a = b;return true;} else return false;}

using ull=unsigned long long;

int main(){
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int T;
    cin>>T;
    while(T--){
        ull A,B,K;
        cin>>A>>B>>K;
        ull l=A*B/gcd(A,B);
        ull ng=0,ok=numeric_limits<ull>::max();
        while(ok-ng>1){
            ull mid=(ok+ng)/2;
            if(mid-mid/A-mid/B+mid/l>=K)ok=mid;
            else ng=mid;
        }
        cout<<ok<<"\n";
    }
}