Hi there. I need some help with this circuit. I want to know if there is a problem with the voltage input.

You should know lm317 is an adjustable voltage regulator. That makes about 1.25V difference between adj and out pins.

Anyway, In lm317's datasheet it says maximum voltage difference : 40V
Does this mean the maximum voltage input is 40v? or what?

Because there will be a voltage drop because of led so voltage difference will be around 2-3v max.

If this circuit is problematic,Can you suggest another adjustable voltage regulator that can handle higher voltages and currents?(and cheap also )

your configuration is for constant current, the maximum current you can draw at 15V difference between Vin & Vout is 2.2A as per datasheet.
since the voltage drop will be very less here, it will work comfortably. calculate the resistance value for 1500 mA or little less. R=1.2/I (may vary litle).
if you see the package getting hot you can provide adiquate heat sink for more discipation.