Solution below.

Reveal solution by highlighting:

A multiple of 15 has the last digit 0 or 5. We can write our 3 digit number as ab0 or ab5.

If ab5 is the correct solution, a+b = 10. The lowest possibility is 1+9. And we’re in luck! 195 = 15*13.

If ab0 is the largest solution, a+b = 15. The lowest possibility is 6+9. 690 is much larger than 195. The solution therefore is 195.