#include <bits/stdc++.h>
#include <cassert>

using namespace std;

typedef long long ll;
typedef long double ld;

// read template
long long readInt(long long l,long long r,char endd){
	long long x=0;
	int cnt=0;
	int fi=-1;
	bool is_neg=false;
	while(true){
		char g=getchar();
		if(g=='-'){
			assert(fi==-1);
			is_neg=true;
			continue;
		}
		if('0'<=g && g<='9'){
			x*=10;
			x+=g-'0';
			if(cnt==0){
				fi=g-'0';
			}
			cnt++;
			assert(fi!=0 || cnt==1);
			assert(fi!=0 || is_neg==false);
			
			assert(!(cnt>19 || ( cnt==19 && fi>1) ));
		} else if(g==endd){
			assert(cnt>0);
			if(is_neg){
				x= -x;
			}
			assert(l<=x && x<=r);
			return x;
		} else {
			assert(false);
		}
	}
}

string readString(int l,int r,char endd){
	string ret="";
	int cnt=0;
	while(true){
		char g=getchar();
		assert(g!=-1);
		if(g==endd){
			break;
		}
		cnt++;
		ret+=g;
	}
	assert(l<=cnt && cnt<=r);
	return ret;
}

long long readIntSp(long long l,long long r){
	return readInt(l,r,' ');
}

long long readIntLn(long long l,long long r){
	return readInt(l,r,'\n');
}

string readStringLn(int l,int r){
	return readString(l,r,'\n');
}

string readStringSp(int l,int r){
	return readString(l,r,' ');
}
// end

const int M = 1e5 + 239;
const int X = 1e6 + 239;

int n, a[M], mn[X];
vector<int> id[X];
vector<int> prime;

void solve()
{                        
	n = readIntLn(1, (int)(1e5));
	for (int i = 0; i < n; i++)
	{
		if (i < n - 1)
			a[i] = readIntSp(1, (int)(1e6));
		else
			a[i] = readIntLn(1, (int)(1e6));
	}
	for (int x : prime) id[x].clear();
	for (int i = 0; i < n; i++)
	{
		while (a[i] > 1)
		{
			int p = mn[a[i]];
			int k = 0;
			while (a[i] % p == 0)
			{
				a[i] /= p;
				k++;
			}
			id[p].push_back(k);
		}
	}
	int ans = 1;
	for (int x : prime)
		if (!id[x].empty())
		{
			int l = 0;
			int r = 0;
			for (int k : id[x]) r = max(r, k + 1);
			int num0 = n - id[x].size();
			while (r - l > 1)
			{
				int h = (l + r) >> 1;
				int now = 0;
				for (int k : id[x]) 
					if (k >= h)
						now += ((k - h) >> 1);
				for (int k : id[x])
					if (k < h)
						now -= (h - k);
				now -= num0 * h;
				if (now >= 0)
					l = h;
				else
					r = h;
			}
			for (int i = 0; i < l; i++) ans *= x;
		}
	cout << ans << "\n";
}

int main()
{ 
	memset(mn, -1, sizeof(mn));
	for (int i = 2; i < X; i++)
		if (mn[i] == -1)
		{
			prime.push_back(i);          
			for (int j = i; j < X; j += i)
				if (mn[j] == -1)
					mn[j] = i;
		}
	int T = readIntLn(1, 5);
	while (T--) solve();		
	assert(getchar() == -1);	
	return 0;
}