A Small Quiz?

Question

Find the least number that fullfils the conditions:
If we divide it by 2 the remeaning will be 1
If we divide it by 3 the remeaning will be 2
If we divide it by 4 the remeaning will be 3
If we divide it by 5 the remeaning will be 4
If we divide it by 6 the remeaning will be 5
If we divide it by 7the remeaning will be 6
If we divide it by 8 the remeaning will be 7
If we divide it by 9 the remeaning will be 8
If we divide it by 10 the remeaning will be 9
If we divide it by 11 the remeaning will be 10
If we divide it by 12 the remeaning will be 11
Good Luck...

Answer 1

The LCM of (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) = 1.

The answer to that is:

2 = 2^1
3 = 3^1
4 = 2^2
5 = 5^1
6 = 2^1 * 3^1
7 = 7^1
8 = 2^3
9 = 3^2
10 = 2^1 * 5^1
11 = 11^1
12 = 2^2 * 3^1

So, the LCM of 2, 3, 4, 5, etc..., 11, 12 is 2^3 * 3^2 * 5^1 * 7^1 * 11^1 = 8 * 9 * 5 * 7 * 11 = 27720. So the number you're looking for is 27719.

Eulercrosser, you did a little miscalculation. Try finding the LCM of all the numbers from 1 to 10. The answer is 2520, not 2530 and ten-elevenths.

Answer 2

if you mean positive integer, it would be 27719 (forgot about 7 at first, and made a small mistake when multiplying by 7).

Just consider the LCM(2,3,4,5,6, 7,8,9,10,11,12)= LCM(5,6,7,8,9,10,11,12) =LCM((5,7,8,9,11)= 27720

Since all of the numbers have a remainder of -1 when divided by the dividend, we simply subtract 1 from the LCM and get 27719

If you mean number with the smallest magnitude, then it would be -1.

All solutions will be of the form 27719•k-1, where k is any integer.

Superbotz, not sure what you mean by your first statement: "LCM of (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11)=1"

Answer 3

Good answer by Euler

Answer 4

The answer is 27719