Question

Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.

Statement R (Reason): HCF is always a factor of LCM.

Options

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of 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 and reason (R) is not the correct explanation of assertion (A).

Explanation:

Given, Product of two numbers = 5780

HCF = 17

We know that

Product of two numbers = HCF × LCM

5780 = 17 × LCM

`5780/17` = LCM

LCM = `5780/17`

LCM = 340

Thus, Assertion is true.

HFC is always a factor of LCM.

This is always true.

Example: For numbers 2 and 3

HCF = 2

LCM = 6

And 2 is a factor of 6

Thus, HCF is always a factor of LCM.

Thus, Reasoning is true.

Now, 

Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.

Statement R (Reason): HCF is always a factor of LCM.

The formula

Product of two numbers = HCF × LCM

is not related to HCF being a factor of LCM

Therefore, Reasoning is not a correct explanation for the Assertion

So,

• Assertion is true
• Reasoning s true
• But, Reasoning is not a correct explanation for Assertion.