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) x LCM (a, b) = a x b. 

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

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

(c) Assertions (A) is true but reason (R) is false. 

(d) Assertions (A) is false but reason (R) is true.

Answer 1

(c) Assertions (A) is true but reason (R) is false. 

Assertion:

The HCF of two numbers is 5 and their product is 150, then their LCM is 30.

HCF = 5 , Product of the numbers = 150 , LCM = 30

We know that

HCF × LCM = Product of the numbers

⇒ 5 × 30 = 150

⇒ 150 = 150

Hence verified

So the assertion is true

Reason:

For any two positive integer a, b HCF (a, b) + LCM (a, b) = a × b

We know that HCF × LCM = Product of the numbers

But it is given that For any two positive integer a, b HCF (a, b) + LCM (a, b) = a × b

So Reason is False.

Answer 2

(c) Assertions (A) is true but reason (R) is false.