The LCM and HCF of two numbers are 105 and 5 respectively. The product of these numbers is ______.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 525
For any two numbers, the product of the numbers equals the product of their HCF and LCM. For each prime factor, the HCF takes the lower of its two powers and the LCM the higher, so between them they hold every prime factor of both numbers as often as the product does.
Product of the numbers \(=\text{HCF}\times\text{LCM}=5\times105=525\)
For example, 15 and 35 have HCF 5 and LCM 105, and \(15\times35=525\).
Tip: The HCF of two numbers always divides their LCM (here \(105=5\times21\)). Use this to test any HCF-LCM pair before working with it.