The LCM of 2 numbers is 2079 and their HCF is 27. If the 1st number is 189, then find the 2nd number.

Answer

To find the second number given the LCM, HCF, and the first number, we can use the relationship between LCM, HCF, and the two numbers. Here's the step-by-step solution:

### Step 1: Write down the relationship
We know that:
\[ \text{LCM} \times \text{HCF} = \text{First Number} \times \text{Second Number} \]
Given:
- LCM = 2079
- HCF = 27
- First Number = 189

### Step 2: Substitute the known values
Substituting the known values into the equation:
\[ 2079 \times 27 = 189 \times \text{Second Number} \]

### Step 3: Calculate the left side of the equation
Now, we need to calculate \(2079 \times 27\):
\[ 2079 \times 27 = 56133 \]

### Step 4: Set up the equation to find the second number
Now we have:
\[ 56133 = 189 \times \text{Second Number} \]

### Step 5: Solve for the second number
To find the second number, we divide both sides by 189:
\[ \text{Second Number} = \frac{56133}{189} \]

### Step 6: Perform the division
Calculating the division:
\[ \text{Second Number} = 297 \]

### Conclusion
Thus, the second number is:
\[ \text{Second Number} = 297 \]