The HCF of two numbers is 6 and their LCM is 26

Answer

To determine whether the statement about the HCF and LCM of two numbers is true or false, we can follow these steps:

### Step 1: Understand the relationship between HCF and LCM
The relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers can be expressed with the formula:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

### Step 2: Substitute the given values
In this case, we know:
- HCF = 6
- LCM = 26

Using the formula:
\[ 6 \times 26 = \text{Product of the two numbers} \]

### Step 3: Calculate the product
Now, let's calculate the product:
\[ 6 \times 26 = 156 \]

### Step 4: Analyze the implications
Now, we need to find two numbers whose HCF is 6 and whose product is 156. We can express the two numbers as:
- Let the two numbers be \( 6a \) and \( 6b \), where \( a \) and \( b \) are coprime (i.e., their HCF is 1).

### Step 5: Set up the equation
From the product we calculated:
\[ 6a \times 6b = 156 \]
This simplifies to:
\[ 36ab = 156 \]

### Step 6: Solve for \( ab \)
Now, divide both sides by 36:
\[ ab = \frac{156}{36} = \frac{13}{3} \]

### Step 7: Evaluate the result
Since \( ab \) must be a whole number (as \( a \) and \( b \) are integers), \( \frac{13}{3} \) is not an integer. This means that there are no such integers \( a \) and \( b \) that satisfy the conditions.

### Conclusion
Since we cannot find two integers that satisfy both the HCF and LCM conditions, the statement is false.