The smallest even number divisible by 6 and 9 is 18.
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1000 is the smallest 4 digit number but of the two factors, it is only divisible by 2. As 999 is obviously divisible by 3 then 999 + 3 = 1002 is also divisible by 3 and, as an even number, is also divisible by 2. The answer is 1002
If a number is not divisible by two then it is not an even number.
The definition of an even number is a number that is divisible by 2. Thus ALL even numbers are evenly (sic) divisible by 2.