The numbers 345111 is divisible by

Let us separately check for each option.

For Option (A),

If 345111 is divisible by 15.

Then, 345111 is also divisible by (5 × 3).

⇒ 345111 is divisible by 5; 345111 is divisible by 3.

Add all digits of the number 345111, we get

3 + 4 + 5 + 1 + 1 + 1 = 15, which is divisible by 3.

⇒ 345111 is divisible by 3.

But clearly, 345111 is not divisible by 5, since the last digit is neither 5 nor 0.

∴ 345111 is not divisible by 15. [∵ it is not divisible by 5]

Option (A) is incorrect.

For Option (B),

If 345111 is divisible by 12.

Then, 345111 is also divisible by (4 × 3).

⇒ 345111 is divisible by 4; 345111 is divisible by 3.

Add all digits of the number 345111, we get

3 + 4 + 5 + 1 + 1 + 1 = 15, which is divisible by 3.

⇒ 345111 is divisible by 3.

But clearly, 345111 is not divisible by 4, since the number ought to be even to get divided by another even number.

∴ 345111 is not divisible by 12. [∵ it is not divisible by 4]

Option (B) is incorrect.

For Option (C),

If 345111 is divisible by 9 then let us check its feasibility.

A number is divisible by 9 if and only if the sum of digits of the number is also divisible by 9.

Sum of digits of 345111 = 3 + 4 + 5 + 1 + 1 + 1

⇒ Sum of digits of 345111 = 15

15 is not divisible by 9.

∴ 345111 is not divisible by 9.

Option (C) is incorrect.

For Option (D),

If 345111 is divisible by 3 then let us check its feasibility.

A number is divisible by 3 if and only if the sum of digits of the number is also divisible by 3.

Sum of digits of 345111 = 3 + 4 + 5 + 1 + 1 + 1

⇒ Sum of digits of 345111 = 15

15 is divisible by 3.

∴ 345111 is divisible by 3.

Option (D) is correct.