A 45-year-old male having a long history of cigarette smoking presented with gangrene of left foot. An amputation of the left foot was done. Representative sections from the specimen revealed the presence of arterial thrombus with neutrophilic infiltrate in the arterial wall. The inflammation also extended into the neighbouring veins and nerves. The most probable diagnosis is:
About other options  
Takayasu's Arteritis :

does not involve the peripheral limb vessels. Its an inflammatory and stenotic disease of medium and large-sized arteries characterized by a strong predilection for the aortic arch and its branches (thus also k/an aortic arch syndrome)

Giant cell arteritis:

also, k/a cranial arteritis or temporal arteritis is a systemic chronic inflammatory vascular disease with many characteristics similar to Takayasu disease
involves medium and large-sized arteries, characteristically one or more branches of the carotid artery, particularly the temporal artery.

Hypersensitivity angiitis

hypersensitivity angiitis also k/a cutaneous vasculitis or leukocytoclastic vasculitis typically involves the small vessels of the skin. Postcapillary venules are most commonly involved vessels; capillaries and arterioles are involved less frequently.
its the most commonly encountered vasculitis in clinical practice.
the hallmark of idiopathic cutaneous vasculitis is the predominance of skin involvement. Skin lesions typically are palpable purpura.
Takayasu arteritis
Giant cell artertis
Hypersensitivity angitis
Thrmoboangitis obliterans