Question

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

Answer 1

The answer is - 6000 - 4000= 2000

Answer 2

Solution :-

To find the numbers between 4000 to 6000 which are divisible by 32, 40, 48 and 60, we have to compute the L.C.M. of 32, 40, 48 and 60

L.C.M. of 32, 40, 48 and 60

32 = 2*2*2*2*2

40 = 2*2*2*5

48 = 2*2*2*2*3

60 = 2*2*3*5

L.C.M. of 32, 40, 48 and 60 = 2*2*2*2*2*3*5 = 480

So, L.C.M. of 32, 40, 48 and 60 is 480

Now, we will find out how many numbers are divisible by 480 between 4000 to 6000

The numbers divisible by 480 between 4000 to 6000 are 4320, 4800, 5280 and 5760

So, only 4 numbers are divisible by 32, 40, 48 and 60 between 4000 to 6000

Answer.