Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40. Reason(R): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × bChoose the correct option.
Question
Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40. Reason(R): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × bChoose the correct option.
Solution
The assertion (A) and the reason (R) are both correct, and (R) is the correct explanation for (A).
Here's why:
Step 1: We know that the product of two numbers is equal to the product of their HCF and LCM. This is given as Reason (R) and is a well-known property in number theory.
Step 2: In this case, the HCF is given as 5 and the product of the numbers is given as 150. So, we can set up the equation 5 * LCM = 150 to find the LCM.
Step 3: Solving for LCM, we get LCM = 150 / 5 = 30.
So, the LCM of the two numbers is 30, not 40 as stated in Assertion (A). Therefore, while the Reason (R) is correct, the Assertion (A) is incorrect.
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