New Brain Teaser – What is that number?

There is a number less than 3000 that when divided by 2 leaves a
remainder of  1, when divided by 3 leaves a remainder of 2, when
divided by 4 leaves a remainder of 3, When divided by 5 leaves a
remainder of 4, when divided by 6 leaves a remainder of 5, and so on up to nine.

What is that number?

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3 Comments

  1. its l.c.m of (2, 3, 4, 5, 6, 7,8 ,9)k – 1
    i found l.c.m = 2520
    and k may be any natural no.
    and reason for subtracting 1 is that is the common difference between every divisor and its corresponding remainder.
    so the ans may be 2519 , 5039 and so on
    but its given the no. should be less than 3000
    so the final answer is 2519.

    its very easy.

  2. 2519. This is how it’s done:

    2=2
    3=3
    4=2×2
    5=5
    6=2×3
    7=7
    8=2x2x2
    9=3×3

    number=2x3x2(we already have a 2 for 4)x5x7(we skiped 6, because the number is a multiple of 6 already)x2x3 – 1.
    why -1?
    because for 2, the smallest number is 2×2-1, for 3 is 3×2-1, for 4 is 4×2-1, and so on.
    the condition is that our number is more than, or equals 10×2-1, and it does.

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