The product of two numbers is 2160 and their HCF is 12 . Find their LCM.

Answer

To find the LCM (Least Common Multiple) of two numbers when their product and HCF (Highest Common Factor) are given, we can use the relationship between these three values. Here’s a step-by-step solution:

### Step 1: Understand the relationship
We know that:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]
In this case, we have:
- Product of the two numbers = 2160
- HCF = 12

### Step 2: Set up the equation
Using the relationship, we can set up the equation:
\[ 12 \times \text{LCM} = 2160 \]

### Step 3: Solve for LCM
To find the LCM, we need to isolate it on one side of the equation. We can do this by dividing both sides by 12:
\[ \text{LCM} = \frac{2160}{12} \]

### Step 4: Perform the division
Now, we will perform the division:
1. First, simplify \( \frac{2160}{12} \):
- Divide 2160 by 12.
- 2160 ÷ 12 = 180

### Step 5: Conclusion
Thus, the LCM of the two numbers is:
\[ \text{LCM} = 180 \]

### Final Answer:
The LCM of the two numbers is **180**.

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