If HCF (150, 210) = 30, then find LCM (150, 210).

Answer

To find the LCM (Least Common Multiple) of the numbers 150 and 210 given that their HCF (Highest Common Factor) is 30, we can use the relationship between LCM, HCF, and the two numbers. The formula is:

\[ \text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} \]

### Step-by-Step Solution:

1. **Identify the numbers and their HCF**:
- Given numbers: \( a = 150 \) and \( b = 210 \)
- Given HCF: \( \text{HCF}(150, 210) = 30 \)

2. **Multiply the two numbers**:
- Calculate \( a \times b \):
\[ 150 \times 210 \]
- To make it easier, we can break it down:
\[ 150 \times 210 = 150 \times (200 + 10) = 150 \times 200 + 150 \times 10 \]
- Calculate each part:
\[ 150 \times 200 = 30000 \]
\[ 150 \times 10 = 1500 \]
- Now add them together:
\[ 30000 + 1500 = 31500 \]

3. **Use the LCM formula**:
- Substitute the values into the LCM formula:
\[ \text{LCM}(150, 210) = \frac{150 \times 210}{\text{HCF}(150, 210)} = \frac{31500}{30} \]

4. **Calculate the LCM**:
- Now divide:
\[ \frac{31500}{30} = 1050 \]

5. **Final answer**:
- Therefore, the LCM of 150 and 210 is:
\[ \text{LCM}(150, 210) = 1050 \]

### Summary:
The LCM of 150 and 210 is **1050**.