Which of the number 12,16,18,20 divides completely the number divisible by both 8 and 3 ?

Options

A. 12
B. 16
C. 18
D. 20

Answer

To solve the problem of which of the numbers 12, 16, 18, and 20 divides completely into a number that is divisible by both 8 and 3, we can follow these steps:

### Step 1: Find the number that is divisible by both 8 and 3.
To find a number that is divisible by both 8 and 3, we calculate the Least Common Multiple (LCM) of these two numbers.

- The prime factorization of 8 is \(2^3\).
- The prime factorization of 3 is \(3^1\).

The LCM is found by taking the highest power of each prime factor:
- For 2, the highest power is \(2^3\).
- For 3, the highest power is \(3^1\).

Thus, the LCM is:
\[ LCM = 2^3 \times 3^1 = 8 \times 3 = 24 \]

**Hint:** To find a number that is divisible by two or more numbers, calculate the LCM of those numbers.

### Step 2: Check which of the given numbers divide 24 completely.
Now we will check each of the numbers (12, 16, 18, and 20) to see if they divide 24 completely.

1. **Check 12:**
\[ 24 \div 12 = 2 \]
Since 2 is a whole number, 12 divides 24 completely.

2. **Check 16:**
\[ 24 \div 16 = 1.5 \]
Since 1.5 is not a whole number, 16 does not divide 24 completely.

3. **Check 18:**
\[ 24 \div 18 \approx 1.33 \]
Since 1.33 is not a whole number, 18 does not divide 24 completely.

4. **Check 20:**
\[ 24 \div 20 = 1.2 \]
Since 1.2 is not a whole number, 20 does not divide 24 completely.

### Conclusion:
The only number from the list that divides 24 completely is **12**.

**Final Answer:** 12