Which artery is closely associated with the vascularity of the lower extremities?

The popliteal artery is the correct choice because it is a critical vessel in the vascular network of the lower extremities. This artery is located behind the knee and acts as a continuation of the femoral artery as it passes into the popliteal fossa. It supplies blood to the lower leg and foot by branching into additional arteries, such as the anterior and posterior tibial arteries.

In contrast, the axillary, subclavian, and carotid arteries are primarily responsible for supplying blood to the upper body and head. The axillary artery supplies the upper limb; the subclavian artery supplies the arms and part of the upper body; and the carotid artery is specifically focused on the blood flow to the head and neck. Therefore, their primary functions do not relate to the vascular needs of the lower extremities, making them less relevant in this context.