The LCM of two numbers is 26, then which of the following can be their HCF?

Options

A. 1
B. 2
C. 13
D. All of these

Answer

To find the possible HCF (Highest Common Factor) of two numbers when their LCM (Lowest Common Multiple) is given, we can follow these steps:

### Step 1: Understand the relationship between LCM and HCF
The relationship between LCM and HCF of two numbers \(a\) and \(b\) is given by the formula:
\[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \]
This means that if we know the LCM, we can determine possible values for the HCF based on the factors of the LCM.

### Step 2: Factor the LCM
The LCM of the two numbers is given as 26. We need to find the prime factorization of 26:
\[ 26 = 2 \times 13 \]
So, the prime factors of 26 are 2 and 13.

### Step 3: Determine the possible HCF values
The HCF must be a factor of the LCM. The factors of 26 are:
- 1
- 2
- 13
- 26

Since the HCF must be a divisor of the LCM, the possible values for the HCF are:
- 1
- 2
- 13

### Step 4: Evaluate the options
If the question provides multiple-choice options, we can check which of these factors are present in the options.

### Conclusion
Based on the factors of 26, the possible HCF values are 1, 2, and 13. Therefore, if the options include any of these numbers, they can be the HCF of the two numbers whose LCM is 26.