Question

Find the greatest number of 4-digit exactly divisible by 12, 16, 24,

28 and 36
​

Answer 1

Step-by-step explanation:

First of all we need to find the L.C.M. (12,16,24,28,36)

12=2*2*3

16=2*2*2*2

24=2*2*2*3

28=2*2*7

36=2*2*3*3

Therefore l.c.m

2*2*3*7*3*2*2=1008

Now greatest no of 4 digit is 9999

Let us divide 9999 by 1008

Then we will have 927 as reminder

So if we subtract 927 from 9999 then the result must be divisible by 1008 i.e the LCM of the given no.s i.e each of the no.s.

So our number will be 9999–927=9072..

∴The greatest 4 digit number exactly divisible by 12, 16, 24, 28 and 36

=9×1008=9072