Echo class depending on Parent category

you probably need to get the parent category of each of the post’s categories first.

<?php
$parent_cat = array();
$post_cats = get_the_category($post->ID);
  foreach( $post_cats as $post_cat ) {
  if( $post_cat->parent ) $parent_cat[] = get_category( $post_cat->parent )->slug;
  }
?>
<article class="post  <?php  
  if ( in_array( 'dream-it', $parent_cat ) ) { echo ' dreamit'; }  
  if ( in_array( 'build-it', $parent_cat ) ) { echo ' buildit'; } 
  if ( in_array( 'get-the-hell-out', $parent_cat ) ) { echo ' getout'; }  ?> ">