#include //#include using namespace std; //using namespace atcoder; //using mint = modint998244353; //const int mod = 998244353; //using mint = modint1000000007; //const int mod = 1000000007; //const int INF = 1e9; const long long LINF = 1e18; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i,l,r)for(int i=(l);i<(r);++i) #define rrep(i, n) for (int i = (n-1); i >= 0; --i) #define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i) #define all(x) (x).begin(),(x).end() #define allR(x) (x).rbegin(),(x).rend() #define P pair template inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t; cin >> t; while (t--) { long long a, b, k; cin >> a >> b >> k; if (a > b)swap(a, b); long long g = gcd(a, b); long long l = lcm(a, b); long long ng = 0; long long ok = LINF * 8; while (1 < abs(ok - ng)) { long long mid = (ng + ok) / 2; auto check = [&]() { long long val = mid; val -= mid / a; if (a != g) { val -= mid / b; val += mid / l; } return val >= k; }; if (check()) ok = mid; else ng = mid; } cout << ok << endl; } return 0; }