#pragma region #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace atcoder; using mint = modint1000000007; //using mint = modint998244353; //using mint = modint; #pragma region using using namespace std; typedef long long ll; using vi = vector; using vvi = vector; using vl = vector; using vvl = vector; using vmint = vector; using vvmint = vector; using pint = pair; using pll = pair; using vpint = vector; using vvpint = vector; using vd = vector; using vvd = vector; //#define rep(i, s, e) for (int(i) = (s); (i) < (e); ++(i)) #define rep(i, e) for (int(i) = 0; (i) < (e); ++(i)) #define rrep(i, s) for (int(i) = (s) - 1; (i) >= 0; --(i)) #define all(x) x.begin(),x.end() #define rall(x) x.rbegin(),x.rend() #pragma endregion #pragma region UnionFind struct UnionFind { vector par; UnionFind(int n) : par(n, -1) {} void init(int n) { par.assign(n, -1); } int root(int x) { if (par[x] < 0) return x; else return par[x] = root(par[x]); } bool issame(int x, int y) { return root(x) == root(y); } bool merge(int x, int y) { x = root(x); y = root(y); if (x == y) return false; if (par[x] > par[y]) swap(x, y); par[x] += par[y]; par[y] = x; return true; } int size(int x) { return -par[root(x)]; } }; #pragma endregion #pragma region GCD ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); } #pragma endregion #pragma region LCM ll lcm(ll a, ll b) { return a / gcd(a, b) * b; } #pragma endregion #pragma region chmin template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } #pragma endregion #pragma region chmax template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } #pragma endregion #pragma region Dijkstra vl dijkstra(vector>> v, int s) { ll INF = 1e18; int MAX = 1e6; vl res(MAX, INF); priority_queue, vector>, greater>> q; q.push({ 0,s }); while (!q.empty()) { int now; ll d; tie(d, now) = q.top(); q.pop(); if (!chmin(res[now], d))continue; for (auto p : v[now]) { int next; ll c; tie(next, c) = p; if (res[next] <= res[now] + c)continue; q.push({ res[now] + c,next }); } } return res; } #pragma endregion #pragma region degからrad double dtor(double deg) { return deg * M_PI / 180; } #pragma endregion #pragma region radからdeg double rtod(double r) { return r * 180 / M_PI; } #pragma endregion //グリッド内チェック bool out(int x, int y, int h, int w) { if (x < 0 || h <= x || y < 0 || w <= y)return true; else return false; } #pragma endregion int main() { ll a, b, k; cin >> a >> b >> k; ll ok = 1e18, ng = 0; while (ok - ng > 1) { ll mid = (ok + ng) / 2; ll l = lcm(a, b); ll tmp = mid / a + mid / b - mid / l; if (tmp >= k)ok = mid; else ng = mid; } cout << ok << endl; }