Find the LCM and HCF of 17, 23 and 29 Using Prime Factorization

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Find the LCM and HCF of the integers 17, 23 and 29 by applying the prime factorization method.

Step 1: Prime Factorization of the Given Integers

17 = 17 (prime number)

23 = 23 (prime number)

29 = 29 (prime number)

Step 2: Find the HCF

There is no common prime factor among 17, 23 and 29.

∴ HCF (17, 23, 29) = 1

Step 3: Find the LCM

LCM is the product of all the given prime numbers:

LCM = 17 × 23 × 29

LCM = 11339

Final Answer

HCF of 17, 23 and 29 = 1
LCM of 17, 23 and 29 = 11339

Conclusion

Thus, by using the prime factorization method, we find that the HCF of 17, 23 and 29 is 1 and their LCM is 11339.