#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;
#define rep(i, n) for(int i=0;i<(n);++i)
#define rep1(i, n) for(int i=1;i<=(n);i++)
#define ll long long
using mint = modint998244353;
using P = pair<ll,ll>;
using lb = long double;
using T = tuple<ll, ll, ll>;
#ifdef LOCAL
#  include <debug_print.hpp>
#  define dbg(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define dbg(...) (static_cast<void>(0))
#endif

int main()
{
    int t;
    cin >> t;
    rep(_,t){
        ll a, b, k;
        cin >> a >> b >> k;
        ll low = 0;
        ll high = 8e18;
        while(high-low>1){
            ll mid = (high+low)/2;
            ll ans = mid/a + mid/b - mid/lcm(a,b);
            ans = mid - ans;
            if(ans>=k) high = mid;
            else low = mid;
        }
        cout << high << endl;
    }
    return 0;
}