Divisible Palindrome

What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15?
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Problem



Palindromic numbers read the same backwards and forwards, e.g. 7227 or 10101.

What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15? 

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.