Final all 3-digit natural numbers which are 12 times as large as the sum of their digits.

There is only one number that exist which is 12 times as large as the sum of their digits, that number is, 108.

Check: Let us take the smallest 3-digit number, say, 100.

Add the digits of 100, we get

1 + 0 + 0 = 1

Multiplying 12 by 1, we get

12 × 1 = 12 ≠ 100

Similarly, check numbers till 999. We will notice that there is only one number that satisfy such condition and that is, 108.

The digits in the number 108 are 1, 0 and 8.

Sum of these digits = 1 + 0 + 8

⇒ Sum of these digits = 9

Now, multiply 12 by 9,

12 × 9 = 108

Hence, the 3-digit natural number which is 12 times as large as the sum of its digit is 108.