Randomize Multiple ul tags by class name using only JavaScript

I have multiple ul elements on my page and I need to add a class name to some and those with that class name need to randomize. I can do it by id but I can only have one id on a page so I can't do that. I need a JavaScript solution without JQuery. Any help is appreciated. Thank you.

Here is what I used to randomize it by id (it only does one ul though):

var thisUL = document.getElementById("myID");
for (var i = thisUL .children.length; i >= 0; i--) {
    thisUL.appendChild(thisUL.children[Math.random() * i | 0]);
}

<ul id="myID">
   <li>random1a</li>
   <li>random1b</li>
   <li>random1c</li>
</ul>

<ul id="myID">
   <li>random2a</li>
   <li>random3b</li>
   <li>random4c</li>
</ul>

<ul id="myID">
   <li>random3a</li>
   <li>random3b</li>
   <li>random3c</li>
</ul>

Each li would need to stay within its own ul.