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

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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.

`7xx11xx13=1001`

`4000+1001=5001`

The number you are searching for is `5001`

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