#include<bits/stdc++.h>
using ll=long long;
using lll=__int128;
using namespace std;
ll a,b,k;
lll like_gcd(lll a,lll b,lll c,lll n)
{
	if(a==0)return b/c*(n+1);
	if(a>=c||b>=c)return n*(n+1)/2*(a/c)+(n+1)*(b/c)+like_gcd(a%c,b%c,c,n);
	lll m=(a*n+b)/c;
	if(m==0)return 0;
	return n*m-like_gcd(c,c-b-1,a,m-1);
}
ll check(lll c)
{
	return like_gcd(a,c%a,b,c/a)+c/a+1;
}
void solve()
{
	scanf("%lld%lld%lld",&a,&b,&k);++k;ll E=__gcd(a,b);
	if(k>(a-1)*(b-1)/2)printf("%lld\n",k+(a-1)*(b-1)/2-1);
	else
	{
		ll l=0,r=a*b;
		while(l<=r)
		{
			ll mid=(l+r)/2;
			if(check(mid)>=k)r=mid-1;
			else l=mid+1;
		}
		printf("%lld\n",(r+1)*E);
	}
}
int main()
{
	int T;scanf("%d",&T);
	while(T--)solve();
	return 0;
}