#ifdef ONLINE_JUDGE
#include <bits/stdc++.h>

#include <atcoder/all>
#else
#include <mylibs/all.h>
#endif

using ll = long long;
using lll = __int128_t;
#define rep(i, n) for (int i = 0, i##_len = (n); i < i##_len; ++i)
#define reps(i, n) for (int i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; --i)
#define rreps(i, n) for (int i = ((int)(n)); i > 0; --i)
#define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
#define repc2(i, s, n) for (int i = (s); i <= (int)(n); i++)
#define length(v) ((int)(v).size())
constexpr int inf = 2'000'000'000;
constexpr ll linf = 4'000'000'000'000'000'000, M7 = 1'000'000'007, M9 = 998'244'353;
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
using namespace std;
using namespace atcoder;

inline ostream& operator<<(ostream& os, lll val) noexcept {
    string s;
    bool neg = val < 0;
    if (val < 0) {
        val *= -1;
    }
    if (val == 0) {
        s += '0';
    } else {
        while (val > 0) {
            s += '0' + val % 10;
            val /= 10;
        }
    }
    reverse(all(s));
    if (neg) s = "-" + s;
    return os << s;
}
inline istream& operator>>(istream& is, lll& val) noexcept {
    string s;
    is >> s;
    bool neg = false;
    if (s[0] == '-') {
        neg = true;
        s = s.substr(1);
    }
    val = 0;
    for (auto c : s) {
        val *= 10;
        val += c - '0';
    }
    if (neg) val *= -1;
    return is;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int Q;
    cin >> Q;
    while (Q--) {
        lll a, b, k;
        cin >> a >> b >> k;
        lll lc = a / gcd(ll(a), ll(b)) * b;
        auto cmp = [&](lll x) -> bool {
            lll cnt = x;
            cnt -= x / a;
            cnt -= x / b;
            cnt += x / lc;
            return cnt >= k;
        };
        auto abs = [](lll x) -> lll { return x < 0 ? -x : x; };
        auto bsearch = [&](auto cmp) {
            lll ok = numeric_limits<lll>::max() / 2, ng = 0;
            while (abs(ng - ok) > 1) {
                lll mid = (ng + ok) / 2;
                if (cmp(mid)) ok = mid;
                else ng = mid;
            }
            return ok;
        };
        cout << bsearch(cmp) << endl;
    }
    return 0;
}