The HCF and LCM of two numbers are 12 and 336 respectively. If one of the number is 84, the other is:

Options

A. 36
B. 48
C. 72
D. 96

Answer

To find the other number when the HCF and LCM of two numbers are given, we can use the relationship between them. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Understand the Relationship**:
We know that the product of the HCF (Highest Common Factor) and LCM (Least Common Multiple) of two numbers is equal to the product of the two numbers. This can be expressed as:
\[ \text{HCF} \times \text{LCM} = N1 \times N2 \]

2. **Substitute the Known Values**:
From the problem, we have:
- HCF = 12
- LCM = 336
- One number (N1) = 84
We need to find the other number (N2). Plugging in these values, we get:
\[ 12 \times 336 = 84 \times N2 \]

3. **Calculate the Left Side**:
First, calculate the product of HCF and LCM:
\[ 12 \times 336 = 4032 \]

4. **Set Up the Equation**:
Now we can set up the equation:
\[ 4032 = 84 \times N2 \]

5. **Solve for N2**:
To find N2, divide both sides of the equation by 84:
\[ N2 = \frac{4032}{84} \]

6. **Perform the Division**:
Now, calculate the value of N2:
\[ N2 = 48 \]

7. **Conclusion**:
Thus, the other number is:
\[ N2 = 48 \]

### Final Answer:
The other number is **48**.