Turn on NumLock on startup in Linux Mint in the Login window

For all versions of Linux Mint

You need to install a program needed for this purpose - numlockx; man page:

sudo apt-get install numlockx

Choose if you wish to achieve the goal through CLI or GUI below.

---

Linux Mint 20.x / 19.x (LightDM)

GUI; probably most convenient under normal operation:

Once numlockx is installed, the following menu item in Login Window -> Settings called:

Activate numlock

becomes available; as you can see:

This will add the line:

activate-numlock=true

to the following file:

/etc/lightdm/slick-greeter.conf

---

Linux Mint 18.x / 17.x (MDM)

GUI; probably most convenient under normal operation:

Once numlockx is installed, the following menu item in Login Window -> Options called:

Enable NumLock

becomes available; as you can see:

As pointed out in the other answer, this will add the following line to /etc/mdm/mdm.conf:

EnableNumLock=true

---

CLI; suitable if you are setting other computers up through SSH, for instance:

Open a text editor you are skilled in with this file, e.g. nano if unsure:

sudoedit /etc/mdm/Init/Default

Add these lines at the beginning of the file:

if [ -x /usr/bin/numlockx ]; then
    /usr/bin/numlockx on
fi

As pointed out by Gilles, don't put exec in front of the command.

When you install numlockx (mentioned by vlastimil above) on Linux Mint 18.3 Cinnamon than the option is called Activate numlock located in System Settings > Login Window > Settings.