I am a 2 digit number.
The digit in tens place and the digit in units place are consecutive prime numbers.
The sum of digits is multiple of 3 and 4.
The number is

The correct option is 57.

Let's analyze the given conditions step-by-step to find the required 2-digit number:

Step 1: Check the sum of digits condition
The problem states that the sum of the digits must be a multiple of both 3 and 4.
The smallest non-zero common multiple of 3 and 4 is $3\times 4=12$.
So, the sum of the digits of the 2-digit number must equal 12 (or a higher multiple of 12, but 12 is the only multiple possible for the sum of two single digits since the maximum sum of two digits is $9+9=18$).

Step 2: Test the given options

Let's test each option against all conditions:

1. Option 57:
- Tens place digit = 5
- Units place digit = 7
- Are 5 and 7 consecutive prime numbers? Yes, 5 and 7 are consecutive prime numbers (the prime numbers sequence is 2, 3, 5, 7, 11...).
- Sum of digits = $5+7=12$.
- Is 12 a multiple of 3 and 4? Yes, $12=3\times 4$.
Thus, 57 satisfies all conditions.

2. Option 23:
- Sum of digits = $2+3=5$ (Not a multiple of 3 or 4).

3. Option 35:
- Sum of digits = $3+5=8$ (Not a multiple of 3).

4. Option 13:
- 1 is not a prime number.
- Sum of digits = $1+3=4$ (Not a multiple of 3).

Therefore, the number is 57.