# Seven Divisibility Disc

*Material Required**: card paper, pen, pencil, scissors*.

Seven divisibility disc contains two discs. First disc contains a number of divisions of a circle and each division contains some digits. The second one has a hole. When the second disc is put on the first certain no. of digits (say 5) can be seen.

Now rotate the second disc on the first disc. Number that can be seen through the hole will be divisible by 7. How it happens?

If you want to make a n digit seven divisibility disc, then the number of divisions you need to make on the first disc are equal to the LCM of n and 6.

For example to make a 5 digit seven divisibility disc first you need to make 30 divisions on the first disc and write a four digit arbitrary number in the four consecutive columns. Divide it by 7 and add the fifth digit to make the 5 digit number divisible by 7. Now take the last four digits if the 5 digit number and add fifth digit to that number to make a number which is divisible by 7. Continue the process and it can be found that after thirtieth digit the same numbers reappear in the same sequence.

why 6 is here? in lcm and 6 ? can you explain please?

We are making a series of 5digit numbers divisible by 7 . So any number such as n and 6 will have LCM which will be smaller to a multiple of 7 by which we will find a number which is required to make it divisible by 7.

I am Mohit