Question

In each of the following numbers, replace M by the smallest number to make resulting number divisible by 3:

(i) 64 M 3

(ii) 46 M 46

(iii) 27 M 53

Answer 1

(i) 64 M 3

The given number = 64 M 3

For a number to be divisible by 3 sum of digits must be divisible by 3

Sum of digits = 6 + 4 + 3 = 13

The number which is divisible by 3 next to 13 is 15

Required smallest number = 15 – 13 = 2

Hence, value of M is 2

(ii) 46 M 46

The given number = 46 M 46

For a number to be divisible by 3 sum of digits must be divisible by 3

Sum of digits = 4 + 6 + 4 + 6 = 20

The number which is divisible by 3 next to 20 is 21

Required smallest number = 21 – 20 = 1

Hence, the value of M is 1

(iii) 27 M 53

The given number = 27 M 53

For a number to be divisible by 3 sum of digits must be divisible by 3

Sum of digits = 2 + 7 + 5 + 3 = 17

The number which is divisible by 3 next to 17 is 18

Required smallest number = 18 – 17 = 1

Hence, the value of M is 1