【Question 14】Select 5 digits from $1 \sim 9$, to form a five-digit number, such that this five-digit number can be evenly divided by any of the 5 selected digits, but cannot be evenly divided by any of the 4 unselected digits. Then, the smallest value of this five-digit number is $\qquad$.

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Note: The blank at the end of the question is intended for the answer to be filled in.
Analysis:
(1) Any five-digit number can be divided by 1, so 1 must be included.
(2) If this five-digit number contains 5, then 5 can only be placed at the end. With 5 at the end, this five-digit number is an odd number, and it definitely cannot be divided by 2, 4, 6, 8, so the five digits of this five-digit number can only be 1, 3, 5, 7, 9. The sum of the digits 1, 3, 5, 7, 9 is 25, which cannot be divided by 3. Therefore, it cannot contain 5.
(3) If 2 and 3 are both present in this five-digit number, then this five-digit number can be divided by 2 and 3, so this five-digit number can also be divided by 6, so it must include 6, so we have four digits: 1, 2, 3, 6; the sum of these four digits is 12, to ensure that this number can be divided by 3, the last digit must also be a multiple of 3, which can only be 9. The sum of the digits 1, 2, 3, 6, 9 is 21, which cannot be divided by 9, so 2 and 3 cannot both appear in this five-digit number.
(4) If this five-digit number does not contain 2, then this five-digit number cannot be divided by 2, so this number cannot have 4, 6, 8. Then the five digits can only be 1, 3, 5, 7, 9. This combination has already been excluded in point 2, so this five-digit number contains 2 but not 3.
(5) Since it does not contain 3, then this five-digit number cannot be divided by 3, so it also does not contain 6, 9. Therefore, this five-digit number does not contain 3, 6, 9, 5, so this five-digit number can only be composed of the digits 1, 2, 4, 7, 8.

The question asks for the minimum value, so we can use trial division. This five-digit number can be divided by 2, so it is an even number. The five-digit even numbers formed by 1, 2, 4, 7, 8 in ascending order are 12478, 12748, 12784, 12874, 14278, 14728, etc.
12478 cannot be divided by 4, 12748 cannot be divided by 8, 12784 cannot be divided by 7, 12874 cannot be divided by 4, 14278 cannot be divided by 4, after testing, 14728 meets the requirements.
Therefore, the minimum value of this five-digit number is 14728.