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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.
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Solution
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.
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