how do I sync my library across all my laptops

Hey Jerome from cape town,

Having the same library on each computer is a nice feature with Apple Music.

To set it up, open the iTunes > Preferences and check the box for iCloud Music Library. Then on your other computers, make sure you are signed into the same Apple ID and turn on the iCloud Music Library for each computer. This will make all the computer have access to the same music. You can view these steps in more detail in the following support article:

Use your Apple Music membership to get your music on all of your devices

Cheers!