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Q.

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


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a

210

b

204

c

208

d

204 

answer is B.

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Detailed Solution

Given are the numbers 28 and 32. We have to find the smallest number which leaves the remainder as 8 and 12, when divided by 28 and 32 respectively.
So, let us subtract the remainders from the given numbers as follows,
28−8=20 32−12=20
Now, we can observe that we get 20 after performing the subtraction, so the smallest number which when divided by 28 and 32 and leaving remainders as 8 and 12 will be,
LCM of (28,32) – 20.
So, the LCM of 28 and 32 is as follows,
28=2×2×7 32=2×2×2×2×2
LCM = 2×2×2×2×2×7=224
Therefore, the smallest number is
224−20=204 .
204 is the smallest number which when divided by 28 and 32 leaves remainder 8 and 12 respectively.
Hence, the correct option is (2).
 
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