A classic motorcycle that would run a combination of a 420 chain and a 44-tooth rear sprocket is likely a vintage small-displacement Japanese bike or a classic 50cc-80cc dirt bike. [1, 2, 3]
Because 420 chains are lightweight and designed for lower horsepower (typically under 15 hp), they were—and still are—commonly used on bikes like the: [1, 2, 3]
