The mystery number is 3.
Step-by-step explanation:
First, we need to find the factors of 4, which are 1, 2, and 4. Since the mystery number is not 1, it must be either 2 or 4.
Next, we need to find the factors of 15, which are 1, 3, 5, and 15. We know that when we pair the mystery number with 15, the LCM is 15. This means that the mystery number and 15 must have a common factor of 15, which eliminates 2 as a possibility since 2 and 15 do not have a common factor.
Therefore, the mystery number must be 3. When we pair 3 with 15, we get 3 and 15 as factors, which have a LCM of 15.