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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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