1. Assertion : The HCF of two numbers is 5 and their product is 150, then their LCM is 30Reason : For any two positive integers a and b, HCF(a,b)+LCM(a,b) =axb.

To prove or disprove the given assertion, we need to follow these steps:

Step 1: Understand the assertion and reason. The assertion states that if the highest common factor (HCF) of two numbers is 5 and their product is 150, then their least common multiple (LCM) is 30. The reason provided is that for any two positive integers a and b, the sum of their HCF and LCM is equal to the product of the two numbers.

Step 2: Check if the given numbers satisfy the conditions. The HCF of the two numbers is given as 5, and their product is given as 150. Let's check if these conditions hold true.

Step 3: Find the prime factorization of the given numbers. To find the prime factorization of 150, we can start by dividing it by the smallest prime number, which is 2. We continue dividing until we cannot divide any further. The prime factorization of 150 is 2 x 3 x 5 x 5.

Step 4: Determine the LCM using the prime factorization. To find the LCM, we need to consider the highest power of each prime factor present in the prime factorization of the given numbers. In this case, the highest power of 2 is 1, the highest power of 3 is 0, and the highest power of 5 is 2. Therefore, the LCM is 2 x 5 x 5 = 50.

Step 5: Compare the calculated LCM with the given LCM. The calculated LCM is 50, while the given LCM in the assertion is 30. Since these values are not equal, the assertion is false.

Step 6: Provide a counterexample. To further support the conclusion that the assertion is false, we can provide a counterexample. Let's consider two numbers, 10 and 15, which have an HCF of 5 and a product of 150. The LCM of these numbers is 30, which is different from the calculated LCM of 50.

Therefore, the given assertion is false, and the reason provided is incorrect.