Posted by **Anthony** on Sunday, September 26, 2010 at 9:57am.

I am thinking of a three-digit number. If you subtract 5 from it, the result is divisible by 5. If you subtract 6 from it, the result is divisible by 6 and if you subtract 7 from it, the result is divisible by 7. What is the smallest number that will satisy these conditions?

- Math -
**Reiny**, Sunday, September 26, 2010 at 10:30am
" If you subtract 5 from it, the result is divisible by 5" ----> number could be 5,10,15,20....

" If you subtract 6 from it, the result is divisible by 6 "

---> number could be 6, 12, 18 , ...

" if you subtract 7 from it, the result is divisible by 7"

---> number could be 7,14

so it must be a multiple of 5,6, and 7

5x6x7 = 210

check:

210 - 5 is divisible by 5

210-6 is divisible by 6

210-7 is divisible by 7

yup! It's 210

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