There is no relationship but you can use them together. Knockout and Backbone are both client side JavaScript Libraries. Laravel is a PHP framework that allows you to build an API that these libraries could use.
Laravel does provide "Form Model Binding": http://laravel.com/docs/html#form-model-binding It won't keep your "divs" in sync but it will allow you to make sure your form is populated with model information.
I would recommend starting here: http://laravel.com/docs
Then head over to Laracasts and watch a view videos to get a better idea. https://laracasts.com
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