#define _USE_MATH_DEFINES
#include<iostream>
#include<vector>
#include<algorithm>
#include<cmath>
#include<string>
#include<iomanip>
#include<numeric>
#include<queue>
#include<deque>
#include<stack>
#include<set>
#include<map>
#include<random>
#include<bitset>
#include<cassert>
#include<complex>
#include<fstream>
#include<cstdlib>
#include<functional>
#include<array>
#include<atcoder/math>
using namespace std;
using namespace atcoder;
typedef long long ll;
const int mod=998244353;
int main(){
	int t,p,q,k;
	cin>>t;
	while(cin>>p>>q>>k){
		int g=gcd(p,q);
		p/=g,q/=g;
		ll cnt=floor_sum(p,p,q,p+q-1);
		if(k>=cnt)
			cout<<(k-cnt+(ll)p*q)*g<<endl;
		else{
			ll ub=(ll)p*q,lb=0;
			while(ub-lb>1){
				ll mid=(ub+lb)/2;
				cnt=floor_sum((mid+q-1)/q,p,q,(mid+q-1)%q+p);
				(cnt>k?ub:lb)=mid;
			}
			cout<<lb*g<<endl;
		}
	}
}