from collections import Counter
import math
def prime_numbers(x):
    if x < 2:
        return []
    prime_numbers = [i for i in range(x)]
    prime_numbers[1] = 0
    for prime_number in prime_numbers:
        if prime_number > math.sqrt(x):
            break
        if prime_number == 0:
            continue
        for composite_number in range(2 * prime_number, x, prime_number):
            prime_numbers[composite_number] = 0
    return [prime_number for prime_number in prime_numbers if prime_number != 0]
primes = prime_numbers(10 ** 2)
def soinnsuu(x):
    s = []
    for i in primes:
        if i > int(math.sqrt(x)):
            break
        elif x % i == 0:
            while x % i == 0:
                x //= i
                s.append(i)
    if not x == 1:
        s.append(x)
    return s
def main():
    import sys
    input = sys.stdin.buffer.readline
    for _ in range(int(input())):
        x = int(input())
        d = Counter(soinnsuu(x))
        cnt = 1
        for k, v in d.items():
            cnt *= v + 1
        for i in range(2, 32):
            d2 = Counter(soinnsuu(i * x))
            cnt2 = 1
            for k, v in d2.items():
                cnt2 *= v + 1
            if cnt2 == cnt * 2:
                print(i * x)
                break
if __name__ == '__main__':
    main()