I routinely write in three languages on a daily basis and have been looking for the CMD+Space shortcut on my K760 for quite some time.
While the Logitech Tablet Keyboard has a specific key for switching language layouts, my K760 sadly though doesn’t. I once accidentally found the shortcut but sadly couldn’t reproduce it afterwards and I’m happy to finally have found it. It’s a huge help for me. I should point out that the shortcut actually seems to be an universal shortcut as it works on the Apple keyboard as well.
This tip and more in the article on Macstories.
After the update to iOS9 the shortcut has changed and is now: