# https://yukicoder.me/problems/no/1611
# No.1611 Minimum Multiple with Double Divisors

# 素因数分解と約数の個数

# X = (p1 ** m1) * (p2 ** m2) * ... * (pk ** mk)
# と素因数分解されたとします． このとき， の正の約数の個数は
# (m1 + 1)(m2 + 1)...(mk + 1) です．


from collections import defaultdict


def prime_factorize(n):
    # 素因数分解 defaultdict
    # 2,3,5,7,11,13,17,19,23,29,31だけ見る
    a = defaultdict(int)
    for i in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]:
        while n % i == 0:
            n //= i
            a[i] += 1
    return a


t = int(input())
for _ in range(t):
    x = int(input())
    p = prime_factorize(x)
    cnt = 1
    for i in p.values():
        cnt *= (i + 1)
    for i in range(2, 32):
        ps = prime_factorize(i)
        dnt = cnt
        for k, v in ps.items():
            dnt = dnt // (p[k] + 1) * (p[k] + v + 1)
        if dnt == cnt * 2:
            print(i * x)
            break