Question

Given that n is a positive integer and b is 3 times n, what is the least common denominator, in terms of n, for the addition of (1)/(b) and (1)/(n) ?

Answer 1

To find the least common denominator (LCD) for the addition of (1/b) and (1/n), we first need to find the factors of both b and n. Since b is 3 times n, the LCD will be the smallest multiple that both b and n have in common. In this example, the least common denominator is 6.

Step-by-step explanation:

The least common denominator (LCD) is the smallest multiple that two or more denominators have in common. In this case, we need to find the LCD for (1/b) and (1/n), where b is 3 times n.

To find the LCD, we first need to find the factors of both b and n.

Since b is 3 times n, we can write it as b = 3n.

Let's consider an example: Suppose n = 2.

Then, b = 3n = 3(2) = 6.

The factors of n = 2 are 1 and 2, and the factors of b = 6 are 1, 2, 3, and 6.

From the factors, we can see that the least common denominator is 6.