Find the LCM and HCF of 40, 36 and 126 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 40, 36 and 126 by applying the prime factorization method.

Step 1: Prime Factorization of the Given Integers

40 = 2 × 2 × 2 × 5 = 2³ × 5

36 = 2 × 2 × 3 × 3 = 2² × 3²

126 = 2 × 3 × 3 × 7 = 2 × 3² × 7

Step 2: Find the HCF

Common prime factors in all three numbers = 2 × 3

∴ HCF (40, 36, 126) = 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 40, 36 and 126 = 6
LCM of 40, 36 and 126 = 2520

Conclusion

Thus, by using the prime factorization method, we find that the HCF of 40, 36 and 126 is 6 and their LCM is 2520.