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?

Answer 1

" 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