9,18
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Itself and any multiples of 9
That's an infinite list.
3, 9, 15
Each common multiple of 9 and 10 occurs exactly once (in the list of common multiples), so there is no common multiple that occurs the most. All common multiples of 9 and 10 are the multiples of their least common multiple which is 90.
"The" five multiples is wrong; there are infinitely many multiples for any number (except zero), not just five. To get those multiples, just use the definition of multiple. That is, you can do any of the following multiplications: 9 x 0 9 x 1 9 x 2 9 x 3 etc., also: 9 x (-1) 9 x (-2) etc.