Q.

Find the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively.


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a

200

b

204

c

203

d

205    

answer is B.

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Detailed Solution

Given to find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.
Calculate the common difference,
288=20 3212=20   Therefore,Common Difference =20  
The smallest positive number that is a multiple of two or more numbers is the LCM of a given number.
Calculate LCM of 28 and 32,  geogebra-export (22)LCM of 28 and 32 is,
LCM=2×2×2×2×2×7 LCM=224  
Therefore, 224 is the LCM of 28 and 32.
Required Number =  LCM of 28 and 32 - Common Factor  22420 204   Thus, the smallest number divisible by 28 and 32 is 204.
Therefore, the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively is 204.
Hence the correct option is 2.
 
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