#include<bits/stdc++.h> using namespace std; typedef long long ll; ll check(ll x,ll n,ll m,ll k){ ll ans=0; ans=x/n+x/m-2*(x/(n*m)); return ans; } int main(){ ll t; scanf("%lld",&t); while(t--){ ll n,m,k; scanf("%lld %lld %lld",&n,&m,&k); ll l=1,r=1e18; while(l<=r){ ll mid=(l+r)/2; if(check(mid,n,m,k)<k){ l=mid+1; }else if(check(mid,n,m,k)){ r=mid-1; }else{ break; } } printf("%lld\n",l); } return 0; }