The relation between L.C.M. and H.C.F. of two positive integers will be

Options

A. H.C.F gt L. C. M
B. H.C.F = L. C. M
C. L.C.M. gt H. C. F.
D. None of these

Answer

To find the relationship between the L.C.M. (Least Common Multiple) and H.C.F. (Highest Common Factor) of two positive integers, we can follow these steps:

### Step 1: Understand the Definitions
- **H.C.F. (Highest Common Factor)**: The largest positive integer that divides both numbers without leaving a remainder.
- **L.C.M. (Least Common Multiple)**: The smallest positive integer that is a multiple of both numbers.

### Step 2: Use the Relationship Formula
There is a well-known relationship between L.C.M. and H.C.F. of two numbers \( a \) and \( b \):
\[ \text{L.C.M.}(a, b) \times \text{H.C.F.}(a, b) = a \times b \]

### Step 3: Example Calculation
Let's take two positive integers, say \( 1 \) and \( 2 \):
- **H.C.F. of 1 and 2**: The only positive integer that divides both is \( 1 \).
- **L.C.M. of 1 and 2**: The smallest positive integer that is a multiple of both is \( 2 \).

Now, substituting into the formula:
\[ \text{L.C.M.}(1, 2) \times \text{H.C.F.}(1, 2) = 1 \times 2 \]
\[ 2 \times 1 = 2 \]

### Step 4: Conclusion
From the example, we see that:
- H.C.F. = 1
- L.C.M. = 2

Thus, we can conclude that L.C.M. is greater than H.C.F. for these two integers.

### Final Statement
The relation between the L.C.M. and H.C.F. of two positive integers is that the L.C.M. is always greater than or equal to the H.C.F., and in this case, it is specifically true that:
\[ \text{L.C.M.} > \text{H.C.F.} \]