A palindrome is a positive integer whose digits are the same when read forwards or backwards. For example, 25352 is a five-digit palindrome. What is the largest five-digit palindrome that is a multiple of 15 ?
An integer is divisible by 15 exactly when it is divisble by both 5 and 3 .

For a positive integer to be divisible by 5 , its units (ones) digit must be 5 or 0 .

For a positive integer to be a palindrome, its first and last digits must be the same.

Since a positive integer cannot have a first digit of 0 , then the first and last digits of a palindrome that is divsible by 5 must be 5 .

Therefore, a five-digit palindrome that is divisible by 15 (and hence by 5 ) must be of the form 5aba5. (Note that the thousands and tens digits must be the same.)

For $5 a b a 5$ to be as large as possible, we start with $a=b=9$.

This gives 59995 which is not divisible by 15 . (To test this, we can use a calculator or use a test for divisibility by 3 , since 59995 is already divisible by 5 .)

The next largest five-digit palindrome of the form $5 a b a 5$ is 59895 , which is divisible by 15 . (If we reduced the value of $a$ rather than the value of $b$, the resulting palindrome would be smaller than this one.)

Therefore, the largest five-digit palindrome that is divisible by 15 is 59895 .

ANSWER: 59895