#include <bits/stdc++.h>

using namespace std;
#define int long long
int32_t main()
{
    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    int t;cin>>t;
    while(t--)
    {
        int a,b,k;cin>>a>>b>>k;int lc=a*b/__gcd(a,b);
        int low=0;int up=8e18;
        while(up-low>1)
        {
            int mid=(low+up)/2;
            int val=mid-(mid/a)-(mid/b)+mid/lc;
            if(val>=k) up=mid;
            else low=mid;
        }
        cout<<up<<'\n';
    }
    return 0;
}