Question 860343
2008, 2006, 2002, are NOT multiples of 3 nor 6, nor 9.  Seeing that both of 18 and 31 are multiples of 3, means that 2008, 2006, 2002 cannot result from your multiplication addition description.  The first listed number, 2007 is apparantly a possibility.  2007 IS a multiple of 9, meaning it is also a multiple of 3.  


You can look further.  2007 is odd, so it is NOT a multiple of 6.  I imagine many possible natural numbers will fit your description.  The question did not ask it, but a particular two numbers is 3 and 93.
{{{18*3+21*93=2007}}};
you may be able to find other combinations of natural numbers which work.