Find the LCM and HCF of 12, 15 and 21 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 12, 15 and 21 by applying the prime factorization method.
Step 1: Prime Factorization of the Given Integers
12 = 2 × 2 × 3 = 22 × 3
15 = 3 × 5
21 = 3 × 7
Step 2: Find the HCF
Common prime factor in all three numbers = 3
∴ HCF (12, 15, 21) = 3
Step 3: Find the LCM
LCM is the product of the highest powers of all prime factors:
LCM = 22 × 3 × 5 × 7
LCM = 420
Final Answer
HCF of 12, 15 and 21 = 3
LCM of 12, 15 and 21 = 420
Conclusion
Thus, by using the prime factorization method, we find that the HCF of 12, 15 and 21 is 3 and their LCM is 420.