#include <stdio.h>
#include <atcoder/all>
#include <bits/stdc++.h>
using namespace std;
using namespace atcoder;
using mint = modint998244353;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf32 1000000001
#define Inf64 2000000000000000001

long long get(long long a,long long b,long long N){
	if(N > a*b - a - b){
		return N - (a-1) * (b-1) / 2;
	}
	long long a0 = N % a;
	long long n = (N-a0)/a + 1;
	if(N==3){
		//cout<<a0<<','<<n<<','<<floor_sum(n,b,a,a0+b)<<endl;
	}
	return floor_sum(n,b,a,a0+b)-1;
}

int main(){
	
	int _t;
	cin>>_t;
	
	rep(_,_t){
		long long p,q,k;
		cin>>p>>q>>k;
		
		long long g = gcd(p,q);
		p /= g;
		q /= g;
		
		long long ok = 0,ng = Inf64;
		while(ng-ok>1LL){
			
			long long mid = (ok+ng)/2;
			if(get(p,q,mid) < k)ok = mid;
			else ng = mid;
			
		}
		long long ans = ok+1;
		ans *= g;
		
		cout<<ans<<endl;
	}
	
    return 0;
}