#include <iostream>
#include <vector>
#include <cmath>
#include <map>
#include <set>
#include <iomanip>
#include <queue>
#include <algorithm>
#include <numeric>
#include <deque>
#include <complex>
#include <cassert>

using namespace std;
using ll = long long;

ll A, B, C, K;

bool judge(ll X){
    return X-(X/A+X/B-X/C) <= K;
}

void solve(){

    cin >> A >> B >> K;
    C = A*B/gcd(A,B);

    ll l=0, r=4e18, c;
    while(r-l>1){
        c = (l+r)/2;
        if (judge(c)) l=c;
        else r=c;
    }

    ll mi=max(1LL, l-5);
    for (ll X=mi; X<=l; X++){
        if (X-(X/A+X/B-X/C) == K && X % A != 0 && X % B != 0){
            cout << X << endl;
            return;
        }
    }

    return;
}

int main(){

    ll T;
    cin >> T;

    while(T){
        T--;
        solve();
    }

    return 0;
}