LCM and HCF of two number are 2079 and 27 respectively. If one number is 297 then find the second number?

Options

A. 189
B. 288
C. 306
D. 403

Answer

To find the second number when the LCM and HCF of two numbers are given, we can use the relationship between LCM, HCF, and the two numbers. The formula we will use is:

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

Given:
- LCM = 2079
- HCF = 27
- One number (let's call it \( a \)) = 297
- The second number (let's call it \( b \)) = \( x \)

### Step 1: Write the formula
Using the formula mentioned above, we can write:

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

Substituting the known values:

\[ 2079 \times 27 = 297 \times x \]

### Step 2: Calculate the left side
Now, we need to calculate \( 2079 \times 27 \):

\[ 2079 \times 27 = 56133 \]

### Step 3: Set up the equation
Now we can set up the equation:

\[ 56133 = 297 \times x \]

### Step 4: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 297:

\[ x = \frac{56133}{297} \]

### Step 5: Perform the division
Now, we perform the division:

\[ x = 189 \]

### Conclusion
The second number is \( 189 \).

### Summary
The second number is \( 189 \).