Question

Assertion (A): For two odd prime numbers x and y, (x ≠ y), LCM (2x, 4y) = 4xy.

Reason (R): LCM (x, y) is a multiple of HCF (x, y).

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

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

Explanation:

The Assertion (LCM (2x, 4y) = 4xy) is proven true using prime factorization. The LCM is found by multiplying the highest powers of all prime factors, which are 2², x, and y. The Reason (LCM is a multiple of HCF) is also true, as it’s a general, fundamental property of all numbers that the HCF always divides the LCM evenly.