A:
UPDATE (to previous answer): Both the Logitech C 270 and the Logitech 920 now work on Windows 10. Prior to this only the 920 had begun working consistently. This is what I did:
1. Plugged in the C 270 only.
2. Logged in to Administrative user account.
3. Opened device manager.
4. Under "imaging" I found the C 270 camera with a yellow edge to the icon, indicating something wrong.
5. Highlighted camera; right click to properties; selected "update driver"
6. Tried the first option -- Browse the Internet...but it did not help.
7. Selected option to do a new Windows update. Two updates were made possible (virus definitions and a security update).
8. Windows downloaded and installed both updates. Restarted computer, as instructed.
9. Logged back in to admin user account. Tested C 270. Did not work.
9. Went online on same user account. Tested C 270 again. It worked!
10. Plugged in Logitech 920. It also worked. Both cameras now worked simultaneously, and one could switch back and forth by clicking an icon on the top left o Microsoft's "Camera" app (free in Microsoft store).
11. Entered a standard user account. Went offline. Both continued to work just the same.
12. The new driver for the C 270 is Microsoft's, and it's called "USB video device." The driver for the 920 is "HD Pro Webcam C920.." They now both appear in Device Manager under a new category called "Cameras."
Hope this can help someone.