Posted by **Joe** on Tuesday, September 16, 2008 at 10:15am.

What is the smallest number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, when divided by 8 leaves a remainder of 7 & so on until when divided by 2 leaves a remainder of 1?

- Math -
**Don**, Tuesday, September 16, 2008 at 11:16am
the smallest number I got was:

2519

- Math -
**David Q**, Tuesday, September 16, 2008 at 1:58pm
I don't believe there's a smaller one than that (I checked it in Excel). The next one is 5039, which is twice the last plus 1. (Incidentally, the one before 2519 corresponds to N=-1.) To work out which number gives a remainder of 1 for all the integers from 1 to P, work out the least common multiple of all the numbers from 2 to P, and subtract 1. So for P=10, the LCM of 2, 3, 4, 5, 6, 7, 8, 9 and 10 is 2x3x2x5x7x2x3=2520; subtract 1 and you get your 2519.

## Answer this Question

## Related Questions

- Math - How many integers between 200 and 500 inclusive leave a remainder 1 when ...
- Math - How many integers bewteen 200 and 500 inclusive leave a remainder 1 when ...
- Math - Find the least positive integer that leaves the remainder 3 when divided...
- Math - Find the smallest positive integer that leaves a remainder of 5 when ...
- math - 1.) when the expression 4x^2-3x-8 is divided by x-a, the remainder is 2. ...
- number theory - Find the least positive integer that leaves the remainder 3 ...
- MATHS - A number has 3 digits. When it is divided by 6 or 7, it leaves a ...
- Mathematics - For what values of m and n Does the expression ( mx^4 + nx^3 + 14x...
- maths - If the integer N leaves a remainder of 1234 when divided by 2013, what ...
- math - 1. A number leaves remainder 6 when divided by 10. What is the remainder ...

More Related Questions