Jawaban:

To find the smallest alliance factor of three numbers, we need to find the greatest common divisor (GCD) of those numbers.

First, let's find the prime factorization of each number:

15 = 3 x 5

20 = 2 x 2 x 5

40 = 2 x 2 x 2 x 5

The common prime factors of these three numbers are 2 and 5. To find the GCD, we take the product of the smallest exponent of each common prime factor.

So, the GCD of 15, 20, and 40 is:

GCD(15, 20, 40) = 2^1 x 5^1 = 10

Therefore, the smallest alliance factor of 15, 20, and 40 is 10.