Let’s solve this math problem by assigning variables to the consecutive integers. Let’s say the first integer is x. Since we are looking for two consecutive integers, the second integer will be x + 1.

We know that the product of these two integers is 182. So, we can set up the equation:

x * (x + 1) = 182

Expanding the equation:

x^2 + x = 182

Rearranging the equation into a quadratic form:

x^2 + x – 182 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let’s solve it by factoring.

Factoring the quadratic equation:

(x – 13)(x + 14) = 0

Setting each factor equal to zero:

x – 13 = 0 or x + 14 = 0

Solving for x in each equation:

x = 13 or x = -14

Therefore, the two consecutive integers whose product is 182 are 13 and 14.