If HCF (a,8)=4 and LCM (a,8) =24, then 'a' is:

Options

A. 14
B. 12
C. 10
D. 8

Explanation

To solve the problem, we need to use the relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers. The formula we will use is:

\[ \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b \]

In this case, we have:
- HCF(a, 8) = 4
- LCM(a, 8) = 24

Let's denote \( a \) as the unknown number we need to find.

### Step 1: Substitute the known values into the formula

Using the formula, we substitute the values we know:

\[ 4 \times 24 = a \times 8 \]

### Step 2: Calculate the left side

Now, calculate the left side:

\[ 4 \times 24 = 96 \]

So we have:

\[ 96 = a \times 8 \]

### Step 3: Solve for \( a \)

To find \( a \), we can divide both sides of the equation by 8:

\[ a = \frac{96}{8} \]

### Step 4: Perform the division

Now, perform the division:

\[ a = 12 \]

### Conclusion

Thus, the value of \( a \) is:

\[ \boxed{12} \]

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