Final answer:
To find the least integer, use the equation x + (x + 2) + (x + 4) + (x + 6) = 180 and solve for x. The resulting value of x will be the least integer.
Step-by-step explanation:
To find the least integer, we need to determine the four consecutive even integers. Let's assume the first even integer is x. The second even integer would be x + 2, the third would be x + 4, and the fourth would be x + 6. The sum of these four integers is 180. So, we have the equation:
x + (x + 2) + (x + 4) + (x + 6) = 180
Simplifying the equation:
4x + 12 = 180
Subtracting 12 from both sides:
4x = 168
Dividing both sides by 4:
x = 42
Therefore, the least integer is 42.