#include <bits/stdc++.h>
using namespace std;

int main() {
    int T;
    cin >> T;
    while (T--) {
        long long X;
        cin >> X;
        vector<int>prime = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97};
        long long ans = 1001001001001001001;
        for(int i = 0; i < prime.size(); i++) {
            long long cnt = X*prime[i];
            long long Y = X;
            bool flag = false;
            while (Y%prime[i] == 0) {
                Y /= prime[i];
                if(10010010010001001001LL/prime[i] < cnt) {
                    flag = true;
                }
                cnt *= prime[i];
            }
            if(flag) {
                continue;
            }
            ans = min(ans,cnt);
        }
        cout << ans << endl;
    }
}