27384 is a member of OEIS A187584: least number divisible by at least n of its digits, different and > 1, here n=5. The sequence can be generated as follows (permalink):

INPUT

L=[2]

record=1

for n in [2..1000000]:

  if is_prime(n)==0:

    D=Set(n.digits())

    sum=0

    for d in D:

      if d != 0 and d>1:

        if n%d==0:

          sum+=1

    if sum>record:

      record=sum

      L.append(n)

      print(n,"=",factor(n))

print()

print(L)

OUTPUT

24 = 2^3 * 3

248 = 2^3 * 31

2364 = 2^2 * 3 * 197

27384 = 2^3 * 3 * 7 * 163

243768 = 2^3 * 3 * 7 * 1451

[2, 24, 248, 2364, 27384, 243768]

27384 is a Harshad number since it is a multiple of its sum of digits (24).

27384 is a nude number because it is divisible by every one of its digits.

27384 is a Lynch-Bell number because its digits are all distinct and it is divisible by each digit. See my blog post titled Lynch-Bell Numbers.

27384 is an untouchable number because it is not equal to the sum of proper divisors of any number.

27384 is a practical number because each smaller number is the sum of distinct divisors of 27384.

27384 is an abundant, pseudoperfect and Zumkeller number.

27384 can be written as a digit equation via:

2 + 7 + 3 = 8 + 4

27384 stabilises after about 275 generations of Conway's Game of Life into two gliders, a single oscillating blinker, five still life blocks, a single still life beehive and a single still life boat.