The LCM ad the HCF of two numbers are 48 and 8, repectively. If one of the numbers is 24, then find the other number.

Answer

To find the other number when the LCM and HCF of two numbers are given, we can use the relationship between them. Here’s a step-by-step solution:

### Step 1: Write down the given values
- LCM (Least Common Multiple) = 48
- HCF (Highest Common Factor) = 8
- One of the numbers (let's call it \( n_1 \)) = 24

### Step 2: Use the relationship between LCM, HCF, and the two numbers
The relationship is given by the formula:
\[ \text{LCM} \times \text{HCF} = n_1 \times n_2 \]
where \( n_1 \) is one number and \( n_2 \) is the other number we need to find.

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 48 \times 8 = 24 \times n_2 \]

### Step 4: Calculate the left side of the equation
Now, calculate \( 48 \times 8 \):
\[ 48 \times 8 = 384 \]
So, we have:
\[ 384 = 24 \times n_2 \]

### Step 5: Solve for \( n_2 \)
To find \( n_2 \), divide both sides of the equation by 24:
\[ n_2 = \frac{384}{24} \]

### Step 6: Perform the division
Now, calculate \( \frac{384}{24} \):
\[ n_2 = 16 \]

### Conclusion
The other number is \( n_2 = 16 \).

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