The product of two numbers is 1280 and their H.C.F. is 8. The L.C.M. of the number will be

Options

A. 160
B. 150
C. 120
D. 140

Answer

To find the L.C.M. of two numbers given their product and H.C.F., we can use the relationship:

\[ \text{H.C.F.} \times \text{L.C.M.} = \text{Product of the two numbers} \]

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Product of the two numbers = 1280
- H.C.F. = 8

2. **Use the Relationship**:
- According to the relationship, we have:
\[ \text{H.C.F.} \times \text{L.C.M.} = \text{Product of the two numbers} \]
- Substituting the known values:
\[ 8 \times \text{L.C.M.} = 1280 \]

3. **Solve for L.C.M.**:
- To find L.C.M., divide both sides of the equation by 8:
\[ \text{L.C.M.} = \frac{1280}{8} \]

4. **Perform the Division**:
- Calculate \( \frac{1280}{8} \):
\[ \text{L.C.M.} = 160 \]

5. **Conclusion**:
- Therefore, the L.C.M. of the two numbers is **160**.