i am a factor of 40

Let's break down the clues given:

1. You are a factor of 40.
2. When paired with 15, the least common multiple (LCM) is 15.
3. You are not 1.

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, and 40. Since you're not 1, we will consider the other factors.

Now let's determine the LCM of a factor of 40 and 15. The formula for LCM can be given in terms of the greatest common divisor (GCD):

\[
\text{LCM}(a, b) = \frac{a \cdot b}{\text{GCD}(a, b)}
\]

Since the LCM with 15 is 15, this means that the LCM (factor, 15) must equal 15. For this to be true, the factor must also divide 15 completely.

The factors of 15 are: 1, 3, 5, and 15. From the factors of 40, the possible candidates are limited to those that are also factors of 15.

Among the factors of 40, the only candidates that are factors of 15 are:
- 1 (but we dismiss this as per your clue)
- 5

Check if 5 fits all your clues:

1. 5 is a factor of 40.
2. The LCM of 5 and 15 is 15:
\[
\text{GCD}(5, 15) = 5
\]
\[
\text{LCM}(5, 15) = \frac{5 \cdot 15}{5} = 15
\]
3. You are not 1.

Thus, the factor you're looking for is **5**.