Here are some clues to a mystery number. - I am a factor of 40 . - When you pair me with 15 , we have an LCM of 15. - I am not 1 .

Step 1 ：The first clue tells us that the mystery number is a factor of 40. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

Step 2 ：The second clue tells us that when paired with 15, the mystery number has an LCM of 15. The LCM of two numbers is the smallest number that is a multiple of both numbers. If the LCM of the mystery number and 15 is 15, then the mystery number must be a factor of 15. The factors of 15 are 1, 3, 5, and 15.

Step 3 ：The third clue tells us that the mystery number is not 1. Therefore, we need to find the common factors of 40 and 15 that are not 1. The common factor is 5.

Step 4 ：Final Answer: The mystery number is \( \boxed{5} \).