Question

Assertion (A): For two prime numbers x and y(x < y), HCF(x, y) = x and LCM (x, y) = y.

Reason (R): HCF (x, y) ≤ LCM (x, y), where x, y are any two natural numbers.

Options

• Both Assertion (A) and Reason (R) are true, and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Assertion (A) is false, but Reason (R) is true.

Explanation:

Assertion (A) is true because for any two distinct prime numbers, the HCF is always one and the LCM is their product (xy), not the numbers themselves; however, Reason (R) is true, as the HCF of any natural numbers is mathematically always less than or equal to their LCM.