Find the smallest distinct positive numbers that provide a counterexample to show the statement is false.

when any number is multiplied by 6 and the digits of the answer are added, the sum will be divisible by 6.

The counterexample is ___.

You coulf d be a genius and instantly see the pattern and answer (I can't), or work out all the possible numbers! Since they want "smallest distinct positive numbers", that would be 1-9:

1 x 6 = 6

6/6 = 1

2 x 6 = 12

(1+2) / 6 = 1/2

3 x 6 = 18

(1+8) / 6 = 3/2

4 x 6 = 24

(2+4) / 6 = 1

... and so on.

You can that not all final numbers are divisible by 6! Like those that are fractions.