Find the LCM and HCF of 84, 90 and 120 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 84, 90 and 120 by applying the prime factorization method.
Step 1: Prime Factorization of the Given Integers
84 = 2 × 2 × 3 × 7 = 22 × 3 × 7
90 = 2 × 3 × 3 × 5 = 2 × 32 × 5
120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
Step 2: Find the HCF
Common prime factors in all three numbers = 2 × 3
∴ HCF (84, 90, 120) = 6
Step 3: Find the LCM
LCM is the product of the highest powers of all prime factors:
LCM = 23 × 32 × 5 × 7
LCM = 2520
Final Answer
HCF of 84, 90 and 120 = 6
LCM of 84, 90 and 120 = 2520
Conclusion
Thus, by using the prime factorization method, we find that the HCF of 84, 90 and 120 is 6 and their LCM is 2520.