#include <bits/stdc++.h>

using namespace std;
using ll = long long;

void solve(){
    ll a, b, c, l;
    cin >> a >> b >> c;
    l = lcm(a, b);
    auto f=[&](ll z){
        return z-z/a-z/b+z/l >= c;
    };
    ll ng = 0, ok = 9e18, mid;
    while(ok-ng>1){
        mid = (ok+ng)/2;
        if (f(mid)) ok = mid;
        else ng = mid;
    }
    cout << ok << endl;
}

int main(){
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);

    int t;
    cin >> t;
    while(t--){
        solve();
    }

    return 0;
}