Rosencrantz and Guildenstern mix red, blue, and white paint in the following ratio:$\text{red}:\text{blue}:\text{white}=3:2:1.$They have $48$ cans of red paint, $40$ cans of blue paint, and $15$ cans of white paint. The cans are all the same size.

What is the greatest number of cans of mixed paint they can make with the same ratio of colors, and why? How much paint of each color will be left over?