Find the LCM and HCF of 26 and 91 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 26 and 91 and verify that LCM × HCF = Product of the integers.

Step 1: Find the HCF of 26 and 91

Prime factorisation:

26 = 2 × 13
91 = 7 × 13

Common factor = 13

∴ HCF (26, 91) = 13

Step 2: Find the LCM of 26 and 91

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

LCM = 2 × 7 × 13 = 182

Step 3: Verify the Given Relation

LCM × HCF = 182 × 13 = 2366

Product of the given integers = 26 × 91 = 2366

Since both values are equal, the relation is verified.

Final Answer

HCF of 26 and 91 = 13
LCM of 26 and 91 = 182

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

Conclusion

Thus, for the integers 26 and 91, the product of their LCM and HCF is equal to the product of the integers themselves.