How to find blog table name in a Multi DB setup?

I have a multisite setup with the Multi DB installed. If I need to manually make an adjustment to a table of a site within the network, what is the best way to find the database that is storing the blog tables.

So lets say I have the 256 db setup and a blog has a table that I need to adjust manually. I need to find that table within 256 db’s. What and how is the best way to go about this?

In the event that you are wondering why I may need to manually adjust a table, is that I am doing API integration with a third party company. During the testing phase I need to check a few things within those individual tables of those sites.