Okay, I understand. You're looking for a budget-friendly PC that can handle League of Legends at 1080p with 60fps. I'll focus the search on prebuilt PCs to keep it simple and affordable.

Okay, I've reviewed the search results. Given your need for a budget PC that can play League of Legends at 1080p 60fps, here are a couple of options that stand out:

First, there's the shinobee® Basic Gaming PC with AMD Ryzen 5 2400G.

Another option is the HP Mini Gaming PC

These PCs should be capable of running League of Legends at 1080p and 60fps, but keep in mind that performance in other games may vary.

Do either of these options seem like a good fit, or would you like me to refine the search with more specific criteria?