Question

Which of the following is true?

• A. \( \text{HCF}(p \times q \times r) \times \text{LCM}(p \times q \times r) = p \times q \times r \)
• B. \( \text{HCF}(p \times q \times r) + \text{LCM}(p \times q \times r) = p \times q \times r \)
• C. \( \text{HCF}(p \times q \times r) \times \text{LCM}(p \times q \times r) \neq p \times q \times r \)
• D. \( \text{HCF}(p \times q \times r) - \text{LCM}(p \times q \times r) = p \times q \times r \)

Hint:

For any set of numbers, the product of the HCF and LCM is equal to the product of the numbers themselves.

Answer 1

The Correct Option is A

Step 1: Understanding HCF and LCM
The HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of two or more numbers have the following property: \[ \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b \] This property holds for any two numbers \( a \) and \( b \). Step 2: Applying to three numbers
Let \( p \), \( q \), and \( r \) be three numbers. Using the property for multiple numbers, we have: \[ \text{HCF}(p, q, r) \times \text{LCM}(p, q, r) = p \times q \times r \] This applies because the product of HCF and LCM of any set of numbers is equal to the product of the numbers themselves. Step 3: Conclusion
Therefore, the correct option is \( (1) \).