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Quantitative Aptitude

HCF and LCM

A number when...

Question

A number when divided by 3,4,5,6,7 gives remainders 2,3,4,5,6 respectively. The smallest such 5 digit number is?

A

10019

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B

10076

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C

11079

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D

10079

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Solution

The correct option is D
10079

Take the LCM of the numbers 3,4,5,6,7. First number to satisfy the given conditions will be LCM-1 = 420-1 = 419

Numbers will fall in an AP with a common difference = LCM

$2^{n d}$ number = 419+420 = 839

$3^{r d}$ = 839+420 = 1259 and so on.

First 5 digit number = 10080-1 = 10079.

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