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23march

A Remainder is chasing me Problem Solution

I just found 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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Solution:


Just take an LCM (least common multiple) of all the numbers in question and subtract 1 from it!
so the LCM of 2,3,4,5,6,7,8,9,10 = 8x9x7x5 = 2520
Hence, the solutions is 2519