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# Find the smallest 4-digit number which is divisible by 18,24 and 32 .

Given :

The given numbers are 18,24 and 32.

To do :

We have to find the smallest 4 digit number that is exactly divisible by 18, 24, and 32.

Solution :

The smallest 4 digit number which is divisible by 18, 24, and 32 will be a multiple of their LCM.

Therefore,

LCM of 18, 24 and 32 is,

$18=2\times 3\times 3$

$24=2\times 2\times 2\times 3$

$32=2\times 2\times 2\times2\times2$

LCM of 18, 24 and 32 $= 2\times 2\times 2\times 2\times 2\times 3\times3 = 288$

Required smallest 4 digit number which is divisible by 18, 24 and 32 is a multiple of 288.

Multiples of 288 are 288, 576, 864,1152,......

The smallest 4 digit number that is exactly divisible by 18, 24 and 32 is 1152.

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