The HCF of two numbers is 27 and their LCM is 162. If one of numbers is 54, what is the other number ?

Options

A. 36
B. 45
C. 9
D. 81

Explanation

To find the other number when given the HCF, LCM, and one of the numbers, we can use the relationship between these values. Here's a step-by-step solution:

### Step 1: Understand the relationship
The relationship between the two numbers (let's call them A and B), their HCF, and their LCM can be expressed as:
\[ A \times B = \text{HCF}(A, B) \times \text{LCM}(A, B) \]

### Step 2: Substitute the known values
From the problem, we know:
- HCF = 27
- LCM = 162
- One number (A) = 54

Now, we can substitute these values into the formula:
\[ 54 \times B = 27 \times 162 \]

### Step 3: Calculate the right side of the equation
First, we need to calculate \( 27 \times 162 \):
\[ 27 \times 162 = 4374 \]

### Step 4: Set up the equation
Now we have:
\[ 54 \times B = 4374 \]

### Step 5: Solve for B
To find B, divide both sides of the equation by 54:
\[ B = \frac{4374}{54} \]

### Step 6: Perform the division
Now, we calculate \( \frac{4374}{54} \):
\[ B = 81 \]

### Conclusion
The other number is \( B = 81 \).

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