I read [this](https://en.wikipedia.org/wiki/Boost_converter) and understood all the derivations for the output voltage and average inductor current for the boost converter in CCM and DCM operation. However, it's not intuitively clear to me why DCM output voltage depends on the load but CCM does not.

I can easily see that from the output voltage expression but what I'm looking for is the intuitive explanation for this.

[![enter image description here](https://i.stack.imgur.com/sI5jm.png)](https://i.stack.imgur.com/sI5jm.png)