import sys
import math
import random

def is_prime(n):
    if n < 2:
        return False
    for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]:
        if n % p == 0:
            return n == p
    d = n - 1
    s = 0
    while d % 2 == 0:
        d //= 2
        s += 1
    for a in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]:
        if a >= n:
            continue
        x = pow(a, d, n)
        if x == 1 or x == n - 1:
            continue
        for _ in range(s - 1):
            x = pow(x, 2, n)
            if x == n - 1:
                break
        else:
            return False
    return True

def pollards_rho(n):
    if n % 2 == 0:
        return 2
    if n % 3 == 0:
        return 3
    if n % 5 == 0:
        return 5
    while True:
        c = random.randint(1, n - 1)
        f = lambda x: (pow(x, 2, n) + c) % n
        x, y, d = 2, 2, 1
        while d == 1:
            x = f(x)
            y = f(f(y))
            d = math.gcd(abs(x - y), n)
        if d != n:
            return d

def factor(n):
    factors = []
    def _factor(n):
        if n == 1:
            return
        if is_prime(n):
            factors.append(n)
            return
        d = pollards_rho(n)
        _factor(d)
        _factor(n // d)
    _factor(n)
    factors.sort()
    return factors

def factorize(n):
    if n == 1:
        return {}
    factors = factor(n)
    res = {}
    for p in factors:
        res[p] = res.get(p, 0) + 1
    return res

def find_smallest_prime_not_dividing(X):
    if X == 1:
        return 2
    for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]:
        if X % p != 0:
            return p
    p = 101
    while True:
        if p * p > X:
            return p
        if X % p != 0 and is_prime(p):
            return p
        p += 2

def solve():
    input = sys.stdin.read().split()
    T = int(input[0])
    for i in range(1, T + 1):
        X = int(input[i])
        if X == 1:
            print(2)
            continue
        factors = factorize(X)
        p_add = find_smallest_prime_not_dividing(X)
        Y_add = X * p_add
        Y_mod = None
        for p in factors:
            e = factors[p]
            current = X * (p ** (e + 1))
            if Y_mod is None or current < Y_mod:
                Y_mod = current
        if Y_mod is None:
            ans = Y_add
        else:
            ans = min(Y_add, Y_mod)
        print(ans)

if __name__ == "__main__":
    solve()