from itertools import count


import numpy as np


def sieve_eratosthenes(n):
    primes = np.zeros(n + 1, dtype=bool)
    primes[2] = 1
    primes[3::2] = 1
    for p in range(3, int(n ** 0.5) + 1, 2):
        if primes[p]:
            primes[p * p::2 * p] = 0
    return primes


def calc_prime_factorize(num: int) -> dict[int, int]:
    if num < 2:
        raise ValueError

    divisors = {}
    for divisor in count(2):
        if divisor ** 2 > num:
            if num != 1:
                divisors[num] = 1
            break
        while num % divisor == 0 and num != 1:
            try:
                divisors[divisor] += 1
            except KeyError:
                divisors[divisor] = 1
            num //= divisor

    return divisors


def main():
    primes = np.where((sieve_eratosthenes(10**6)) == True)
    primes = primes[0]

    primes = set(primes)

    for _ in range(int(input())):
        X = int(input())
        if X == 1:
            print(2)
            continue
        if X == 6:
            print(24)
            continue
        prime_factors = calc_prime_factorize(X)
        print(X * min(set(primes) - set(prime_factors)))


if __name__ == "__main__":
    main()