Find the LCM and HCF of 404 and 96 and Verify LCM × HCF = Product of the Integers

Video Explanation

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Solution

Question: Find the LCM and HCF of the pair of integers 404 and 96 and verify that LCM × HCF = Product of the integers.

Step 1: Find the HCF of 404 and 96

Prime factorisation:

404 = 2 × 2 × 101 = 2² × 101
96 = 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3

Common factor = 2²

∴ HCF (404, 96) = 4

Step 2: Find the LCM of 404 and 96

LCM is the product of the highest powers of all prime factors:

LCM = 2⁵ × 3 × 101

LCM = 9696

Step 3: Verify the Given Relation

LCM × HCF = 9696 × 4 = 38784

Product of the given integers = 404 × 96 = 38784

Since both values are equal, the relation is verified.

Final Answer

HCF of 404 and 96 = 4
LCM of 404 and 96 = 9696

∴ LCM × HCF = Product of the integers is verified.

Conclusion

Thus, for the integers 404 and 96, the product of their LCM and HCF is equal to the product of the integers themselves.