#include <bits/stdc++.h>
using namespace std;

#define endl "\n" 
#define int long long

const int MOD = 998244353;

void solve() {
    int a, b, k; cin >> a >> b >> k;
    int l = 1, r = LONG_LONG_MAX;
    while (l < r) {
        int mid = l + (r - l) / 2;
        int count = mid - mid / a - mid / b + mid / (lcm(a, b));
        if(count < k) {
            l = mid + 1;
        } else {
            r = mid;
        }
    }
    cout << l << endl;
}

int32_t main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T = 1;
    cin >> T;
    while (T--) {
        solve();
    }
    return 0;
}