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Q.

Find the least number which when divided by 52, 78, 117 leaves remainders 33, 59 and 98 respectively.

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a

452

b

469

c

458

d

449

answer is D.

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Detailed Solution

Difference of 52 & 33 = 19

Difference of 78 & 59 = 19

Difference of 117 & 98 = 19

∴  Require  number=LCM  of  (52,78,117)−19

⇒LCM  of  52,78,117=468

So  least  number  is  required=468−19=449

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