That would be the same as the smallest four-digit even number: 1,000, which also happens to be the smallest four-digit whole number.
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It is: 1005
Oh, what a delightful little puzzle we have here! To find a four-digit number that is divisible by both 8 and 9, we can look for a number that is divisible by their least common multiple, which is 72. So, let's find a multiple of 72 that is a four-digit number, like 1008. Such a harmonious number, don't you think?
The smallest four digit number is 1000. It is even so 1001 is the smallest four digit number that is odd.
1008 is the lowest four-digit number divisible by 36, and 9972 is the highest.
If you allow non integers, then your smallest four-digit number would be .0001. If you only allow integers, then your smallest four-digit number would be 1000. Your largest four-digit number would be 9999.