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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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