You can mix different speed RAM sticks, but both will run at the slower speed.
Yes, it works. The motherboard will detect the slower stick and run both at that speed. If you have a 3200MHz stick and add a 2666MHz stick, they’ll both run at 2666MHz.
You might also lose dual-channel if the timings or ranks don’t match. The system will still boot and run, but you’re leaving performance on the table. Most people won’t notice the difference in everyday use, but if you’re gaming or doing memory-intensive work, it’s worth buying a matching pair.
So it’s fine for a spare parts build or a quick capacity boost. For a clean system, spend the extra $20 on a matched kit.
