#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define lll long long//__int128
#define pii pair<int,int>
//#define f first
#define s second
# define pi 3.14159265358979323846
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;

struct chash_key
{
    ll operator()(pii x) const { return (ll)x.first*1000000000   + x.second; }
};
//gp_hash_table<pii,int,chash_key> hs[2],p[2];

//gp_hash_table<ll,int> dp;

/*
ios_base::sync_with_stdio(false);
cin.tie(0),cout.tie(0);

cout << fixed;
	cout.precision(3);
	cout << x << '\n';
*/
struct P
{
    int x,y,z;
    bool operator <(const P &a)const
    {
        return y>a.y;
    };
};

int a,b,c;

const ll mod=998244353;


 //sum (ai+b)/c for i=0 to n
 long long FloorSumAP(long long a, long long b, long long c, long long n){
  //cout<<a<<b<<c<<n<<"\n";

  if(!a) return (b / c) * (n + 1);
  if(a >= c or b >= c) return ( ( n * (n + 1) ) / 2) * (a / c) + (n + 1) * (b / c) + FloorSumAP(a % c, b % c, c, n);
  long long m = (a * n + b) / c;
  return m * n - FloorSumAP(c, c - b - 1, a, m - 1);
}


int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0),cout.tie(0);

    int ttt;
    cin>>ttt;


    for(int tt=1;tt<=ttt;tt++)
    {
        cin>>a>>b>>c;
        ll x=1,y=(ll)a*c;
        int g=__gcd(a,b);
        ll L=(ll)a*b/g;

        for(;x<y;)
        {
            ll h=(x+y)/2;

            if(h/(2*L)>c*((L/a+1)*(L/b+1)-1))
            {
                y=h-1;
                continue;
            }
            ll d=h/(2*L)*((L/a+1)*(L/b+1)-1);
            ll e=(h%(2*L));

            if(e<L)
            d+=FloorSumAP(a,e%a+b,b,e/a);
            else d+=FloorSumAP(a,e-L+a+b,b,L/a-1);
            d--;
            if(d<c) x=h+1;
            else y=h;
        }

        cout<<x<<"\n";
    }
    //cout<<FloorSumAP(3,4%3+4,4,4/3)<<" "<<FloorSumAP(3,5%3+4,4,5/3);

}