Question

Find the smallest 4-digit number which is exactly
divisible by 18. 24 and 32.
INCERT pls give me answer fast​

Answer 1

LCM of 18 , 24 and 32 :

18 = 2 x 3 x 3

24 = 2 x 2 x 2 x 3

32 = 2 x 2 x 2 x 2 x 2

LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288

The smallest four digit number that is divisible by 288 :

We know that as 288 is LCM of 18 , 24 and 32 so it must be divisible be these numbers .

So , from the table of 288 :

288 x 4 = 1152

Here , 1152 is the first four digit number that occurs in 288 .

Since 288 is divisible by 18, 24 and 32 , 1152 is also divisible by all these numbers .

Therefore , 1152 is the smallest four digit number divisible by 18, 24 and 32 .