The product of two numbers is 5040 and their HCF is 12. Find their LCM.

Answer

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

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

### Step 2: Write down the known values
From the problem, we know:
- The product of the two numbers (A × B) = 5040
- The HCF of the two numbers = 12

### Step 3: Substitute the known values into the formula
Using the formula:
\[ 5040 = 12 \times \text{LCM} \]

### Step 4: Solve for LCM
To find the LCM, we can rearrange the equation:
\[ \text{LCM} = \frac{5040}{12} \]

### Step 5: Perform the division
Now, we calculate:
\[ \text{LCM} = \frac{5040}{12} = 420 \]

### Conclusion
Thus, the LCM of the two numbers is **420**.

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