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2014-08-05T19:37:21+05:30

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It is easy.  take the LCM of the given numbers.
3, 8, 16        3 ,  2x 2 x 2    ,  2 x 2 x 2 x 2
so  3* 2^4 = 48 is the LCM
smallest 3 digit number is 100. check for the reminder when 100 is divided by 48
reminder = 100 - 2* 48 = 4. 
So it means 100  =  n * 48 + 4
if we want to make LHS divisble by 48, we have to increase RHS by 44  (48-4). then the reminder will vanish.
so 144 = (n+1) 48

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2014-08-05T21:43:39+05:30

3, 8, 16        3 ,  2x 2 x 2    ,  2  x  2  x  2 x  2
so  3* 2^4 = 48 is the L C M
small  3 digit number is 100. check for the reminder when 100 is divided by 48
r = 100 - 2* 48 = 4.  
So it means 100  =  n * 48 + 4 
if we want to make LHS divisble by 48, we have to increase RHS by 44  (48-4). then the reminder will vanish.
so 144 = (n+1) 48 
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