How many numbers are there between 4000 and 6000 which are exactly divisible by 32, 40, 48 and 60?

LCM of 32, 40, 48 and 60 = 480
The number divisible by 480 between 4000 and 6000 are 4320, 4800, 5280 and 5760.
Hence, required number of numbers are 4.