To find the next palindrome number after 72927, we need to check each of the given options sequentially to see which one is a palindrome.
- 74047: This reads the same forwards and backwards, so it is a palindrome.
- 73537: This also reads the same forwards and backwards, so it is a palindrome.
- 72937: This does not read the same forwards and backwards (72937 vs 73927), so it is not a palindrome.
- 73037: This also reads the same forwards and backwards, so it is a palindrome.
Now we have found three palindromes: 74047, 73537, and 73037.
The least of these values that is greater than 72927 is 73037.
Thus, the next palindrome number that the odometer will show is 73037.