Let the four consecutive even integers be represented as \( x, x+2, x+4, x+6 \).
To find the sum of these integers, we can set up the equation:
\[ x + (x + 2) + (x + 4) + (x + 6) = 324 \]
Simplifying the left side, we combine like terms:
\[ 4x + 12 = 324 \]
Next, we isolate \( x \) by subtracting 12 from both sides:
\[ 4x = 324 - 12 \] \[ 4x = 312 \]
Now, divide both sides by 4:
\[ x = \frac{312}{4} \] \[ x = 78 \]
Thus, the four consecutive even integers are:
- \( x = 78 \)
- \( x + 2 = 80 \)
- \( x + 4 = 82 \)
- \( x + 6 = 84 \)
The least of these integers is \( x \), which is:
\[ \boxed{78} \]