If the product of two numbers is 3360 and their LCM is 96, then their HCF is:

Options

A. 35
B. 33
C. 34
D. 29

Answer

To find the HCF (Highest Common Factor) of two numbers given their product and LCM (Least Common Multiple), we can use the relationship between these three quantities. The formula we will use is:

\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]

Given:
- Product of the two numbers = 3360
- LCM = 96

We need to find the HCF.

### Step 1: Write down the formula
We know that:
\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]

### Step 2: Substitute the known values
Substituting the known values into the formula:
\[ 96 \times \text{HCF} = 3360 \]

### Step 3: Solve for HCF
To find the HCF, we can rearrange the equation:
\[ \text{HCF} = \frac{3360}{96} \]

### Step 4: Perform the division
Now we will perform the division:
\[ \text{HCF} = \frac{3360}{96} = 35 \]

### Conclusion
Thus, the HCF of the two numbers is 35.