#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rep1(i, n) for (int i = 1; i <= (n); i++)
#define rrep(i, n) for (int i = n - 1; i >= 0; i--)
#define rrep1(i, n) for (int i = n; i >= 1; i--)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define eb emplace_back
#define fi first
#define se second
#define sz(x) (int)(x).size()
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
typedef long long int ll;

void speedUpIO() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
}

template <class T> bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template <class T> bool chmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}
/*--------------------------------------------------*/
typedef pair<int, int> P;

const int INF = 1e9;
const ll LINF = 4e18;
const int MX = 100010;

ll solve() {
    ll a, b, k;
    cin >> a >> b >> k;
    ll ok = 1, ng = LINF;
    while (ng - ok > 1) {
        ll mid = (ok + ng) / 2;
        ll cnt = mid / a;
        cnt += mid / b;
        cnt -= mid / lcm(a, b);
        cnt = mid - cnt;
        if (cnt <= k) {
            ok = mid;
        } else {
            ng = mid;
        }
    }
    return ok;
}

int main() {
    speedUpIO();
    int t = 1;
    cin >> t;
    while (t--) {
        // solve();
        cout << solve() << "\n";
        // cout << (solve() ? "YES" : "NO") << "\n";
        // cout << fixed << setprecision(15) << solve() << "\n";
    }
    return 0;
}