How to get a random multiple of a given number within a range

I'm making a program in which a JPanel is created with a random RGB value and the user has to use buttons to match the color in another JPanel.

I want the random R, G, and B values to be multiples of 15, though, so the user can match the color more easily.

Right now my code looks like this:

int randRed = rand.nextInt(255);

and the same for green and blue. I could use a modulus to repeat the code until it happens to be a multiple of 15 but that would be terribly inefficient.

What is the best method to achieve a random multiple of 15 less than 255?