## Thursday, March 23, 2006

### Smallest Integer

What is the smallest positive integer that leaves a remainder of 1 when divided by 2, remainder of 2 when divided by 3, a remainder of 3 when divided by 4, … and a remainder of 9 when divided by 10?

#### 1 comment:

1. As all the numbers leave a remainder which is one less than the number i.e, 8 leaves 7, 6 leaves 5 etc ... which suggests that the unknown number +1 should be divisible by all the numbers..... and hence taking the Least Common Multiple of numbers from 2 through 9 which is 2520 is the first possible number which is divisible by all the numbers and so answer would be 2520-1=2519

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