LCM of two numbers is 2079 and their HCF is 27. If one of the number is 189, the other number is :

Options

A. 297
B. 584
C. 189
D. 216

Answer

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

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

Given:
- LCM = 2079
- HCF = 27
- One number (Number 1) = 189
- Other number (Number 2) = x (unknown)

### Step-by-Step Solution:

1. **Write the formula**:
\[ \text{LCM} \times \text{HCF} = \text{Number 1} \times \text{Number 2} \]
Substitute the known values:
\[ 2079 \times 27 = 189 \times x \]

2. **Calculate LCM × HCF**:
\[ 2079 \times 27 \]
To do this, we can calculate:
\[ 2079 \times 27 = 56133 \]

3. **Set up the equation**:
Now we have:
\[ 56133 = 189 \times x \]

4. **Solve for x**:
To find x, divide both sides by 189:
\[ x = \frac{56133}{189} \]

5. **Perform the division**:
Calculate:
\[ x = 297 \]

### Conclusion:
The other number is **297**.