Latest comments from each category?

Hello all,
I’ve been banging my head on this topic over the last few days and hope I find a godsent in these forums.

I’m trying to achieve the following on restaurants review site:

On homepage I’m trying to display the most recently commented-on post for each category.

I managed to display the most recently published post for each category, but if an older post from each category gets a comments, that post should be bumped to the top of the list with that latest comment displayed.

Any help on this will be greatly appreciated

Kind regards,
pff