Everyone is busy these days, so realistically you most likely won't get LinkedIn recommendations from your colleagues without asking them. That is why you need to take matters into your own hands and request recommendations yourself.
Why you need recommendations
First of all, recommendations are an excellent way to confirm your listed skills.
Everyone can see your recommendations, including recruiters and HR professionals who usually pay great attention to your Recommendations section. By getting recommendations from the people who know you professionally, you will raise your profile and enhance your chances of being noticed and deemed trustworthy.
How to Request recommendations
Recommendations are extremely powerful as they can validate what you've written about yourself so you should definitely spend some time asking for them, on a regular basis.