The product of the LCM and the HCF of two numbers is 24. If the difference of the numbers is 2, then the greater of the number isa.8b.6c.3d.4

The problem states that the product of the LCM and the HCF of two numbers is 24 and the difference between the two numbers is 2.

Let's denote the two numbers as a and b, with a being the greater number.

According to the problem, we have two equations:

1. LCM(a, b) * HCF(a, b) = 24
2. a - b = 2

We know that for any two numbers, the product of their LCM and HCF is equal to the product of the numbers themselves. So, we can write:

a * b = 24

We also know that a - b = 2. We can solve this equation for a:

a = b + 2

Now we can substitute a in the first equation:

(b + 2) * b = 24 b^2 + 2b - 24 = 0

This is a quadratic equation and we can solve it by factoring:

(b - 4)(b + 6) = 0

The solutions are b = 4 and b = -6. Since b cannot be negative, we discard -6. So, b = 4.

Substitute b = 4 into the equation a = b + 2, we get a = 6.

So, the greater number is 6. Therefore, the answer is b.6.