The sum of two consecutive odd integer is 56. What is the smaller (first) integer?

Let the first odd integer be \( x \). Since we are talking about consecutive odd integers, the next odd integer will be \( x + 2 \).

According to the problem, the sum of these two integers is 56:

\[ x + (x + 2) = 56 \]

Simplifying this equation:

\[ 2x + 2 = 56 \]

Now, subtract 2 from both sides:

\[ 2x = 54 \]

Next, divide both sides by 2:

\[ x = 27 \]

Thus, the smaller (first) integer is \( \boxed{27} \).