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A number is divisible by 9 if the sum of the digits is a multiple of 9. Now 1+9+5+6=21 and 27 is the nearest multiple the we have to add 6 hence the number becomes 1962.

We need to add 6 because sum of digits is equal to 21. If it should be divisible by 9 then the sum of the number should be a multiple should be of 9. the nearest multiple of 9 for 21 is 27. So, 6 should be added to 1956 ie 1962 to prove that there will be no remainder.