#include <bits/stdc++.h>

using namespace std;

const int maxl = (int)1e6 + 10;

int lp[maxl];
int cnt[maxl];
vector <int> d[maxl];

bool can(int n, int md, const vector <int> &d) {
    int need = md * (n - (int)d.size());
    for(int x: d) {
        if (x < md) need += md - x;
        else need -= (x - md) / 2;
    }
    return need <= 0;
}

int main() {
    lp[1] = 1;
    for(int i = 2; i < maxl; ++i) {
        if (lp[i] > 0) continue;
        for(int j = i; j < maxl; j += i) {
            if (lp[j] == 0) lp[j] = i;
        }
    }
    ios_base::sync_with_stdio(0);
    int t;
    cin >> t;
    while(t--) {
        int n;
        cin >> n;
        memset(cnt, 0, sizeof cnt);
        for(int i = 1; i < maxl; ++i) {
            d[i].clear();
        }
        for(int i = 0; i < n; ++i) {
            int x;
            cin >> x;
            while(x > 1) {
                int p = lp[x];
                int c = 0;
                while(x > 1 && x % p == 0) x /= p, c++;
                d[p].push_back(c);
                cnt[p] += c;
            }
        }
        int gcd = 1;
        for(int p = 2; p < maxl; ++p) {
            if (cnt[p] < n) continue;
            int lf = -1, rg = 20;
            while(rg - lf > 1) {
                int md = (lf + rg) / 2;
                if (md == -1 || can(n, md, d[p])) {
                    lf = md;
                } else rg = md;
            }
            //lf now is the maximum power of p in gcd
            while(lf--) gcd *= p;
        }
        cout << gcd << '\n';
    }
    return 0;
}