The ratio of two numbers is 4 : 3 and their HCF is 8. Find their LCM.
A. 48
B. 96
C. 64
D. 84

Options

A. C
B. B
C. A
D. D

Answer

To find the LCM of two numbers given their ratio and HCF, we can follow these steps:

### Step 1: Define the numbers using the ratio
Let the two numbers be represented as:
- First number = 4x
- Second number = 3x

### Step 2: Use the given HCF to find the value of x
We know that the HCF (Highest Common Factor) of these two numbers is given as 8. Since the HCF of 4x and 3x is x (because x is the common factor), we can set up the equation:
- x = 8

### Step 3: Calculate the actual numbers
Now, substituting the value of x back into the expressions for the numbers:
- First number = 4x = 4 * 8 = 32
- Second number = 3x = 3 * 8 = 24

### Step 4: Calculate the LCM using the relationship between HCF and LCM
We can use the relationship between HCF, LCM, and the product of the two numbers:
\[ \text{HCF} \times \text{LCM} = \text{First number} \times \text{Second number} \]
Substituting the known values:
\[ 8 \times \text{LCM} = 32 \times 24 \]

### Step 5: Calculate the product of the two numbers
Calculating the product:
\[ 32 \times 24 = 768 \]

### Step 6: Solve for LCM
Now, substituting back into the equation:
\[ 8 \times \text{LCM} = 768 \]
To find LCM, divide both sides by 8:
\[ \text{LCM} = \frac{768}{8} = 96 \]

### Conclusion
Thus, the LCM of the two numbers is **96**.