HCF of two numbers is 28 and their LCM is 336. If one number is 112, then the other number is

Options

A. 98
B. 56
C. 70
D. 84

Answer

To find the other number when the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) are given, we can use the relationship between HCF, LCM, and the two numbers. The formula is:

\[ \text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2} \]

Given:
- HCF = 28
- LCM = 336
- One number (Number 1) = 112

Let the other number be \( X \).

### Step 1: Write the formula
Using the formula, we can set up the equation:

\[ 28 \times 336 = 112 \times X \]

### Step 2: Calculate the left side
Now, calculate \( 28 \times 336 \):

\[ 28 \times 336 = 9408 \]

### Step 3: Set up the equation
Now we have:

\[ 9408 = 112 \times X \]

### Step 4: Solve for \( X \)
To find \( X \), divide both sides of the equation by 112:

\[ X = \frac{9408}{112} \]

### Step 5: Perform the division
Now, calculate \( \frac{9408}{112} \):

\[ X = 84 \]

### Conclusion
The other number is \( 84 \).