Final answer:
The most common complication of a supracondylar fracture is injury to the brachial artery or nerves, potentially leading to Volkmann's ischemic contracture, a permanent disability.
Step-by-step explanation:
The most common complication associated with a supracondylar fracture, which is a type of fracture of the humerus just above the elbow joint, is injury to the brachial artery or nerves near the fracture site. This complication is significant because it can lead to a condition known as "Volkmann's ischemic contracture," which is a permanent flexion contracture of the hand at the wrist, resulting in a claw-like deformity. Treatment and timely detection are critical to prevent such permanent disability.