Make sure you have also updated your web browser and you're running Firefox version 57.0.4 or newer, as that has mitigation that makes it impossible for JavaScript on websites to exploit these bugs. Average home users only run untrusted code in their web browser so this mitigation is key to being safe from these bugs.
For more information also see Security notice: Meltdown and Spectre
Instructions for LMDE 2:
- Find the level 4 security updates for packages
Linux kernel 3.16.51-3+deb8u1
andlinux-libc-dev
; they should have a new version 3.16.51-3+deb8u1 or newer - Mark them for installation and install them; I'd suggest you install all level 4 Linux updates
- Reboot your system