This challenging problem can be taken to different stages by different children, but offers a starting point for all. Pupils should be encouraged to play with the interactivity and explore what happens. Drawing their ideas together will enable the class to offer some hypotheses and then they can test out their ideas. The problem is in fact about common factors (in the number of "teeth"), but some
children may be happy to stick to cogs of the same size.
If the interactivity is not available, you might like to print off this sheet of cogs
and cut them out for the pupils to use practically, or for you to demonstrate on an OHP.