The LCM and HCF of two number are 2079 and 27 respectively. Accordingly. If one number of which is 189. Find the another number?

Options

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

Answer

To find the other number when one number is given along with the LCM and HCF, we can use the relationship between LCM, HCF, and the two numbers. The formula states that:

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

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

We can set up the equation:

\[ 2079 \times 27 = 189 \times x \]

Now, let's solve for x step by step:

### Step 1: Calculate the product of LCM and HCF
First, we need to calculate \( 2079 \times 27 \).

\[ 2079 \times 27 = 56133 \]

### Step 2: Set up the equation
Now, we can substitute this value into our equation:

\[ 56133 = 189 \times x \]

### Step 3: Solve for x
To find x, we can rearrange the equation:

\[ x = \frac{56133}{189} \]

### Step 4: Perform the division
Now, we will perform the division:

\[ x = 297 \]

### Conclusion
Thus, the other number is \( \boxed{297} \).

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