using namespace std;
#include<bits/stdc++.h>
void _main();int main(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(30);_main();return 0;}
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
typedef long long ll;typedef long double ld;
#define rep1(a)          for(int i = 0; i < (a); i++)
#define rep2(i, a)       for(int i = 0; i < (a); i++)
#define rep3(i, a, b)    for(int i = (a); i < (b); i++)
#define rep4(i, a, b, c) for(int i = (a); i < (b); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define ALL(x) std::begin(x),std::end(x)
#define rALL(x) std::rbegin(x),std::rend(x)
#define INF ((1LL<<62)-(1LL<<31))
#define bit(x,i) (((x)>>(i))&1)
#define fi first
#define se second
#define pb push_back
#define Endl endl
#define spa " "
#define YesNo(x) cout<<(x?"Yes":"No")<<endl;

#include <atcoder/all>
using namespace atcoder;

//コンパイル時の引数にBLUEBERRYを渡すとdeb関数が使える
#ifdef BLUEBERRY
#define deb print
#else
#define deb 
#endif
//！？！？
#define O print
//可変長引数で入力を受け取りつつ変数を宣言
inline void scan(){}
template<class Head,class... Tail>
inline void scan(Head&head,Tail&... tail){std::cin>>head;scan(tail...);}
#define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;scan(__VA_ARGS__)
//vectorのcin
template<typename T>
std::istream &operator>>(std::istream&is,std::vector<T>&v){for(T &in:v){is>>in;}return is;}
//vectorのcout
template<typename T>
std::ostream &operator<<(std::ostream&os,const std::vector<T>&v){for(auto it=std::begin(v);it!=std::end(v);){os<<*it<<((++it)!=std::end(v)?" ":"");}return os;}
//x,y,x,yを渡すとldで距離を返す
long double my_distance(long double xi,long double yi,long double xj,long double yj){return sqrt(abs((xi-xj)*(xi-xj))+abs((yi-yj)*(yi-yj)));}
//可変長引数のprint関数
void print(){cout << '\n';}
template<class T, class... Ts>
void print(const T& a, const Ts&... b){cout << a;(cout << ... << (cout << ' ', b));cout << '\n';}
//可変長引数のmin
template<class... T>
constexpr auto min(T... a){return min(initializer_list<common_type_t<T...>>{a...});}
//可変長引数のmax
template<class... T>
constexpr auto max(T... a){return max(initializer_list<common_type_t<T...>>{a...});}
template<typename T,typename U>inline bool chmax(T&a,U b){if(a<b){a=b;return 1;}return 0;}
template<typename T,typename U>inline bool chmin(T&a,U b){if(a>b){a=b;return 1;}return 0;}
//Union-Find from https://zenn.dev/reputeless/books/standard-cpp-for-competitive-programming/vi((b%2==0?b-1:b)+2-(a%2==0?a+1:a))/2er/union-find
class UnionFind{public:UnionFind()=default;explicit UnionFind(size_t n):m_parentsOrSize(n, -1){}int find(int i){if(m_parentsOrSize[i]<0){return i;}return(m_parentsOrSize[i]=find(m_parentsOrSize[i]));}void merge(int a,int b){a=find(a);b=find(b);if(a!=b){if(-m_parentsOrSize[a]<-m_parentsOrSize[b]){std::swap(a,b);}m_parentsOrSize[a]+=m_parentsOrSize[b];m_parentsOrSize[b]=a;}}bool connected(int a,int b){return (find(a)==find(b));}int size(int i){return -m_parentsOrSize[find(i)];}private:std::vector<int>m_parentsOrSize;};

//こめんとを付け外ししてMODを切り替える
//ll MOD = INF;
ll MOD = 1000000007;
//ll MOD = 998244353;

//回文判定 
bool iskaibun(string s){ll k = s.size();rep(i,0,k/2){if(s[i]!=s[k-1-i]){return false;}}return true;}

//二部グラフ判定 重みなしグラフを引数に取り、boolを返す
bool isbipartite_graph(vector<vector<ll>>&g){ll v = g.size();vector<ll>col(v,-1);vector<bool>used(v,false);bool ret = true;rep(i,v){if(used[i])continue;col[i]=0;[DFS([&](auto&&f,ll pos,ll pr)->void{if(used[pos])return;used[pos]=true;for(auto to:g[pos]){if(to==pr)continue;if(used[to]&&col[pos]==col[to]){ret = false;return;}if(used[to])continue;col[to]=col[pos]^1;f(f,to,pos);}}),&i]{DFS(DFS,i,-1);}();}return ret;}
//a~bの和 a<b
ll ran(ll a,ll b){return ((a+b)*(b-a+1))/2;}
//Pythonにあるreplaceみたいなもの 森久保さん作
string replace(const string&moto,const string &from,const string&too){int from_len = from.size();string tmp=from+moto;int tmp_len=tmp.size();vector<int>za=atcoder::z_algorithm(tmp);string ret="";for (int i=from_len;i<tmp_len;){if(za[i]>=from_len){ret+=too;i += from_len;}else{ret += tmp[i];i++;}}return ret;}
//座圧する
ll zaatu(vector<ll>&A){map<ll,ll>m;for(auto&&x:A)m[x]=0;ll ret = 0;for(auto&&[key,val]:m)val=ret++;for(auto&&x:A)x=m[x];return ret;}
//約数列挙　引数に取った整数の約数のvectorを返す
vector<ll>enumdiv(ll n){vector<ll>s;for(ll i = 1;i*i<=n;i++){if(n%i==0){s.push_back(i);if(i*i!=n)s.push_back(n/i);}}return s;}
//トポロジカルソート グラフ、入次数カウント、頂点数を引数で渡すと、トポロジカルソートされた頂点列を返す
vector<ll> topo_sort(vector<vector<ll>>&G,vector<ll>&nyu_cnt,ll v){vector<ll>ret;priority_queue<ll,vector<ll>,greater<ll>>pq;rep(i,0,v){if(nyu_cnt[i]==0)pq.push(i);}while(!pq.empty()){ll pos = pq.top();pq.pop();for(ll i:G[pos]){nyu_cnt[i]--;if(nyu_cnt[i]==0)pq.push(i);}ret.push_back(pos);}return ret;}
//素因数分解 pair<素数、指数>のvectorを返す
vector<pair<ll,ll>> soinsu_bunkai(ll x){vector<pair<ll,ll>>ret;rep(i,2,sqrt(x)+1){if(x%i==0){ll cnt{};while(x%i==0){x/=i;cnt++;}ret.push_back({i,cnt});}}if(x!=1)ret.push_back({x,1});return ret;}
//二項係数MOD MODは上の方で設定、MAXまでのnCrをCOM(n,r)でとれる
const int MAX = 5000000;
ll fac[MAX], finv[MAX], invv[MAX];
void COMinit(){fac[0]=fac[1]=finv[0]=finv[1]=invv[1]=1;for(int i=2;i<MAX;i++){fac[i]=fac[i-1]*i%MOD;invv[i]=MOD-invv[MOD%i]*(MOD/i)%MOD;finv[i]=finv[i-1]*invv[i]%MOD;}}
ll COM(int n,int k){if(n<k)return 0;if(n<0||k<0)return 0;if(k==0)return 1;return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;}
ll nPr(int n,int k){if(n<k)return 0;if(n<0||k<0)return 0;if(k==0)return 1;return fac[n]*(finv[n-k]);}
//エラトステネスの篩　isprimeには素数かどうかが入っている
vector<bool> isprime;vector<int> Era(int n) {isprime.resize(n, true);vector<int> res;isprime[0] = false; isprime[1] = false;for (int i = 2; i < n; ++i) isprime[i] = true;for (int i = 2; i < n; ++i){if (isprime[i]) {res.push_back(i);for (int j = i*2; j < n; j += i) isprime[j] = false;}}return res;}


using mint = modint998244353;

void solve();
void _main(){
    int testcase = 1;
    cin >> testcase;
    for(;testcase--;){
        solve();
    }
}
void solve(){
    LL(a,b,k);
    ll ok = 0,ng = INF;
    ll g = lcm(a,b);
    while(abs(ok-ng)>1){
        ll mid = (ok+ng)/2;
        ll cna = mid/a,cnb = mid/b,cnab = mid/(g);
        if(mid-(cna+cnb-cnab)<=k)ok=mid;
        else ng = mid;
    }
    O(ok);
}