Painting a Prism Twice

Mark has 60 unit cubes. He arranges the cubes to form a $3\times 4\times 5$ rectangular prism, and paints all external faces of the prism red. He removes the cubes with less than 2 painted sides. Finally, he completely submerges the resulting solid in a tub of yellow paint. At least how many square units of paint were applied to the solid?