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The product of the LCM and the HCF of two numbers is 24. If the difference of the numbers is 2, then the greater of the number is
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- 3
- 4
- 6
- 8
Correct Option: C
Let the larger number be p.
We can find the required answer with the help of given formula ,
Product of two numbers = HCF × LCM
∴ Smaller number = p – 2
∴ First number × Second number = HCF × LCM
⇒ p (p – 2) = 24
⇒ p2 – 2p – 24 = 0
⇒ p2 – 6p + 4p – 24 = 0
⇒ p (p – 6) + 4 (p – 6) = 0
⇒ (p – 6) (p + 4) = 0
⇒ p = 6 because p ≠ – 4
Hence , the greater number is 6.
