Cartesian products aren't things that help 😉 This is a cartesian product:

SELECT <stuff> FROM LargeTable1 CROSS JOIN LargeTable2

You get a huge resultset with a number of row equal to the product of the row counts in each table (hence cartesian product). It's a great way to kill a server.

Is a table redesign not an option? It really, really would make stuff like this far easier.