When are the best times to post on LinkedIn?

To reach the largest number of users with your content avoid evenings, late afternoons, and weekends.
It only makes sense to publish when people are around. LinkedIn has found their busiest times to be morning and midday, Monday through Friday. 

That's not to say other times during the work week aren't going to work for you. These are just guidelines to help you achieve higher viewership, so give different times a try and test your success.