Math

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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 -

    " 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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