Step-by-step explanation:

Let's call the two consecutive odd integers "x" and "x+2". We can set up two equations based on the given information:

1. The product of the two integers is 15:

x(x+2) = 15

2. Their sum is 8:

x + (x+2) = 8

Now, we can solve this system of equations. First, simplify the second equation:

2x + 2 = 8

Subtract 2 from both sides:

2x = 6

Divide by 2:

x = 3

Now that we know the value of x, we can find the second integer:

x + 2 = 3 + 2 = 5

So, the two consecutive odd integers are 3 and 5.