find the smallest number when divided by 2,3,4,5,6 leaves remainder 1,2,3,4,5

Asked by my3shyll | 9th Jul, 2016, 06:07: PM

Expert Answer:

Here,
2 - 1 = 1
3 - 2 = 1
4 - 3 = 1
5 - 4 = 1
6 - 5 = 1
That is, if we subtract 1 from the number divisible by 2, 3, 4, 5, 6, we get the required number.
The smallest number divisible by 2, 3, 4, 5, 6 will be the LCM of 2, 3, 4, 5, 6.
LCM of 2,3, 4, 5, 6 is
 
begin mathsize 16px style The space smallest space number space divisible space by space 2 comma space 3 comma space 4 comma space 5 space and space 6 space
equals space LCM space of space 2 comma space 3 comma space 4 comma space 5 space and space 6
equals 2 cross times 3 cross times 4 cross times 5 cross times 6
equals 60
So comma space the space required space number space which space leaves space straight a space remainder space of space 1 comma space 2 comma space 3 comma space 4 comma space 5
equals LCM space of space left parenthesis 2 comma space 3 comma space 4 comma space 5 comma space 6 right parenthesis minus 1
equals 59 end style

Answered by Rebecca Fernandes | 10th Jul, 2016, 08:09: PM