A Guide to Finding the Lowest Common Denominator (LCD) and Adding/Subtracting Fractions

lowest common denominator (LC. d)

The lowest common denominator (LCD) is the smallest multiple that two or more denominators have in common

The lowest common denominator (LCD) is the smallest multiple that two or more denominators have in common. It is used when we want to add or subtract fractions with different denominators.

To find the LCD, you need to consider the prime factors of each denominator and then take the highest power of each prime factor that appears in any denominator.

Let’s go through an example:

Find the LCD of the fractions 2/3 and 5/6.

First, list the prime factors of each denominator:
– 3 = 3^1
– 6 = 2^1 * 3^1

Now, take the highest power of each prime factor. In this case, we have:
– 2^1
– 3^1

Multiply these highest powers together to find the LCD:
LCD = 2^1 * 3^1 = 2 * 3 = 6

So, the LCD of 2/3 and 5/6 is 6.

To add or subtract fractions with different denominators, we need to convert them to have the same denominator. In this case, we need to convert 2/3 and 5/6 to fractions with a denominator of 6 (the LCD).

For the fraction 2/3, we can multiply both the numerator and denominator by 2 to get:
2/3 * 2/2 = 4/6

For the fraction 5/6, we don’t need to do anything since the denominator is already 6.

Now that both fractions have the same denominator, we can add or subtract them:
4/6 + 5/6 = (4 + 5)/6 = 9/6

However, the answer is not simplified since both 9 and 6 have a common factor of 3. We can simplify by dividing both the numerator and denominator by 3:
9/6 = (3*3)/(2*3) = 3/2

So, the final answer is 3/2.

More Answers: