Question

Assertion (A): The HCF of two numbers is 7 and their LCM is 70. If one of the numbers is 14 then the other number is 30.

Reason (R): For any two given positive integers a and b, we have \[\text{HCF},(a, b) \times \text{LCM},(a, b) = (a \times b).\]

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 a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is false and Reason (R) is true.

Explanation:

Step 1 – Assertion: A is false. Using the stated relationship, the other number is \[\frac{7 \times 70}{14}=35\], not 30.

Step 2 – Reason: R is true. For any two given positive integers a and b, we have \[\text{HCF},(a, b) \times \text{LCM},(a, b) = (a \times b).\]