Find the LCM and HCF of the of the following integers by applying the prime factorisation method.
17, 23 and 29

Answer

To find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of the integers 17, 23, and 29 using the prime factorization method, we can follow these steps:

### Step 1: Prime Factorization of Each Number
- **17**: Since 17 is a prime number, its prime factorization is \( 17^1 \).
- **23**: Since 23 is also a prime number, its prime factorization is \( 23^1 \).
- **29**: Similarly, 29 is a prime number, so its prime factorization is \( 29^1 \).

### Step 2: Identify the HCF
The HCF is found by taking the product of the lowest powers of all prime factors common to the numbers.
- In this case, there are no common prime factors among 17, 23, and 29.
- Therefore, the HCF is \( 1 \).

### Step 3: Identify the LCM
The LCM is found by taking the product of the highest powers of all prime factors present in the numbers.
- The prime factors are \( 17^1 \), \( 23^1 \), and \( 29^1 \).
- Thus, the LCM is calculated as:
\[ LCM = 17^1 \times 23^1 \times 29^1 = 17 \times 23 \times 29 \]

### Step 4: Calculate the LCM
Now, we will calculate the product:
- First, calculate \( 17 \times 23 \):
\[ 17 \times 23 = 391 \]
- Now, multiply the result by 29:
\[ 391 \times 29 = 11339 \]

### Final Answers
- **HCF**: \( 1 \)
- **LCM**: \( 11339 \)