Question

1 (Assertion): If HCF(a,b) =4 and ab + 96×404, then LCM (a,b) =9696

2(Reason): LCM of two numbers a and b= HCF (a,b) × ab.

Answer 1

The assertion and reason given are not correct.

The assertion states that if the highest common factor (HCF) of numbers a and b is 4 and ab + 96 = 404, then the least common multiple (LCM) of a and b is 9696. However, this is not necessarily true. The HCF and LCM of two numbers are independent of each other, and the given equation ab + 96 = 404 does not provide enough information to determine the LCM.

The reason given states that the LCM of two numbers a and b is equal to the product of their HCF and their product (ab). This is incorrect. The correct relationship is that the LCM of two numbers is equal to the product of the numbers divided by their HCF. In other words, LCM(a, b) = (a * b) / HCF(a, b).

Therefore, both the assertion and reason are incorrect.