The HCF of two numbers is 6 and the product of two numbersis 360. Find theLCM of the numbers

Options

A. 60
B. 30
C. 12
D. 6

Answer

To find the LCM of two numbers when the HCF (or GCD) and the product of the numbers are given, we can use the relationship between these three values. Here’s how to solve the problem step by step:

### Step 1: Understand the relationship
The relationship between the LCM (Least Common Multiple), HCF (Highest Common Factor), and the product of two numbers is given by the formula:
\[ \text{LCM}(A, B) \times \text{HCF}(A, B) = A \times B \]

### Step 2: Identify the given values
From the question, we know:
- HCF (A, B) = 6
- Product of the numbers (A × B) = 360

### Step 3: Substitute the values into the formula
We can rearrange the formula to find the LCM:
\[ \text{LCM}(A, B) = \frac{A \times B}{\text{HCF}(A, B)} \]

Substituting the known values:
\[ \text{LCM}(A, B) = \frac{360}{6} \]

### Step 4: Perform the calculation
Now, calculate the right side:
\[ \text{LCM}(A, B) = \frac{360}{6} = 60 \]

### Step 5: State the final answer
Thus, the LCM of the two numbers is:
\[ \text{LCM} = 60 \]

---