Can you find it?

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A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It’s not a small number, but it’s not really big, either.
When I looked for a smaller number with this property I couldn’t find one.

Can you find it?

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  • 1 Answer(s)

    2519


    LCM – HCF  = 2520 -1 


    Other approach
    The number has to end in 9.
    Looked brute force for small numbers.
    59 and 119 were promising, but no cigar.

    Then looked for agreement among
    39 + multiples of 40,
    69 + multiples of 70 and
    89 + multiples of 90
    Smallest one was 2519.

    anikam Expert Answered on 24th August 2015.
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