Find the smallest positive multiple of $9$ with all even digits.

The answer is 288.

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A number is divisible by 9 only if its digits sum 9, or a multiple. Due to no sum of numbers of the same parity gives as a result an odd, we look for the smallest even multiple of 9, which is 18. Then, we look for the combination of smallest digits that gives this sum, which are 2, 8 and 8. Hencefore, the number is 288