from copy import deepcopy def factorization(n): arr = [] temp = n for i in range(2, int(-(-n**0.5//1))+1): if temp%i==0: cnt=0 while temp%i==0: cnt+=1 temp //= i arr.append([i, cnt]) if temp!=1: arr.append([temp, 1]) if arr==[]: arr.append([n, 1]) return arr T = int(input()) P = [] for i in range(2,100000): flg = True for j in range(2,int(i**0.5)+1): if i%j == 0: flg = False break if flg: P.append(i) for _ in range(T): X = int(input()) F = factorization(X) P_cp = deepcopy(P) n = 10**18 for i in range(len(F)): f = F[i][0] if f == 1: continue m = F[i][1] n = min(n,f**(m+1)) P_cp.remove(f) n = min(n,P_cp[0]) print(X*n)