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

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200

204

203

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,

28 − 8 = 20 32 − 12 = 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,

L C M = 2 × 2 × 2 × 2 × 2 × 7 L C M = 224

Therefore, 224 is the LCM of 28 and 32.

Required Number =  LCM of 28 and 32 - Common Factor ⇒ 224 − 20 ⇒ 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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