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find the least number which becomes  divisible by 7,11 and 13 when 4000 is subtracted...

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shewa55 | Valedictorian

Posted May 4, 2013 at 12:48 PM via web

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find the least number which becomes  divisible by 7,11 and 13 when 4000 is subtracted from it.

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted May 4, 2013 at 1:59 PM (Answer #1)

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Since 7, 11 and 13 are prim numbers the least number divisible by all of them is their product, that is

`7cdot11cdot13=1001`

Now we add 4000 and your result is 5001.

If you subtract 4000 from 5001 you get 1001 which is the smallest natural number divisible by 7, 11 and 13.

Alternatively you cloud use congruences.

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oldnick | Valedictorian

Posted May 4, 2013 at 2:10 PM (Answer #2)

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`7xx11xx13=1001`

`4000+1001=5001`

 

The number you are searching for is  `5001`    

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