If g and l are L.C.M. and H.C. F. of two positive integers, then the relation will be :

Options

A. g gt l
B. g lt l
C. g = l
D. None of these

Answer

To solve the problem, we need to establish the relationship between the Least Common Multiple (LCM) and the Highest Common Factor (HCF) of two positive integers. Let's denote the two positive integers as \( a \) and \( b \).

### Step-by-Step Solution:

1. **Define the Terms**:
- Let \( G \) be the LCM of \( a \) and \( b \).
- Let \( L \) be the HCF of \( a \) and \( b \).

2. **Use the Relationship**:
- There is a well-known relationship between LCM and HCF of two numbers:
\[ G \times L = a \times b \]
This means that the product of the LCM and HCF of two numbers is equal to the product of the numbers themselves.

3. **Analyze the Relationship**:
- Since \( G \) (LCM) is the smallest number that both \( a \) and \( b \) can divide into, and \( L \) (HCF) is the largest number that can divide both \( a \) and \( b \), we can conclude that:
\[ G \geq L \]
This indicates that the LCM is always greater than or equal to the HCF for any two positive integers.

4. **Conclusion**:
- Therefore, the relationship can be summarized as:
\[ G \geq L \]
This means that the LCM of two positive integers is always greater than or equal to their HCF.

### Final Relation:
Thus, the relation between the LCM \( G \) and HCF \( L \) of two positive integers \( a \) and \( b \) is:
\[ G \geq L \]