Listing secondary categories on product page?

Once I navigate to a product, I want to be able to see what other categories it is listed under. Does anyone know how I would go about doing this?

I need it done this way because when I sell ink cartridges, for each cartridge, there are a few compatible printers as well.

So when a customer goes to the main product page, the need to be able to see a list of other secondary categories that it is compatible with.

Anyone know how to do this? Thank you!

im having this same problem, the website im wtorking on is for motorcycles.

For instant. i have an oil filter. i would like for people to see what other bikes it fits, the only thing i have come up with is just put it in the description. but we have over 30,000 products and thats alot of typing to do to fill that in under each product, gota be an easier way