Find the LCM and HCF of 510 and 92 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 510 and 92 and verify that LCM × HCF = Product of the integers.
Step 1: Find the HCF of 510 and 92
Prime factorisation:
510 = 2 × 3 × 5 × 17
92 = 2 × 2 × 23
Common factor = 2
∴ HCF (510, 92) = 2
Step 2: Find the LCM of 510 and 92
LCM is the product of the highest powers of all prime factors:
LCM = 22 × 3 × 5 × 17 × 23
LCM = 23460
Step 3: Verify the Given Relation
LCM × HCF = 23460 × 2 = 46920
Product of the given integers = 510 × 92 = 46920
Since both values are equal, the relation is verified.
Final Answer
HCF of 510 and 92 = 2
LCM of 510 and 92 = 23460
∴ LCM × HCF = Product of the integers is verified.
Conclusion
Thus, for the integers 510 and 92, the product of their LCM and HCF is equal to the product of the integers themselves.