#include <iostream>
#include <vector>
#include <cmath>
#include <map>
#include <set>
#include <iomanip>
#include <queue>
#include <algorithm>
#include <numeric>
#include <deque>
#include <complex>
#include <cassert>

using namespace std;
using ll = long long;

int N=11;
vector<ll> p = {2,3,5,7,11,13,17,19,23,29,31};

void solve(){
    ll X, Y, e, cx=1, cy=1;
    cin >> X;
    Y = X;
    for (int i=0; i<N; i++){
        e = 0;
        while(Y % p[i] == 0){
            Y /= p[i];
            e++;
        }
        cx *= (e+1);
    }

    for (int i=2; i<=31; i++){
        Y = X*i; cy=1;
        for (int j=0; j<N; j++){
            e = 0;
            while(Y % p[j] == 0){
                Y /= p[j];
                e++;
            }
            cy *= (e+1);
        }
        if (cy == cx * 2){
            cout << X*i << endl;
            return;
        }
    }
}

int main(){

    int T;
    cin >> T;
    while(T){
        T--;
        solve();
    }

    return 0;
}