Learning how to find common denominators is an essential
skill for every math student. This

handout will provide a step-by-step approach to finding common denominators.

Before learning how to find common denominators, it is important to understand
least common

multiples and how they work.

**Least Common Multiple -** Multiples of a number are the products of the
number and the

numbers 1, 2, 3, 4, 5 . . . . In other words,

and so on.

The least common multiple (LCM) is the smallest common
multiple that two or more numbers

share. For instance, the least common multiple of the numbers 4 and 6 is **12**.

Least common multiples are necessary when finding common
denominators because they are

needed in order to find the lowest common denominator (LCD) of a fraction. The
LCD is

needed when operations such as addition and subtraction are being performed and
the fractions

contain denominators that are not the same.

**To find the least common denominator**

To add fractions with unlike denominators, first the fractions must be rewritten
as equivalent

fractions with a common denominator. The common denominator is found by
identifying the

least common multiple of the denominators of the fractions. The following is a
step-by-step

explanation of how to do this.

**Add:**

**Step 1: Create a multiples table for the denominators.**

In the exercise, the denominators for the fractions are 2 and 3. In order to
find the lowest

common denominator for the two fractions, the least common multiple of the two
numbers must

be found.

The least common multiple for 2 and 3 is **6**. When
working with fractions, the least common

multiple is often called the least common denominator. Both terms refer to the
same thing.

**Step 2: Rewrite the original fractions as equivalent fractions with a common
denominator.**

• To rewrite as an equivalent fraction with
a denominator of 6, begin by placing the 6 in the denominator slot

of the equivalent fraction.

• Then, using the multiples table, identify what number,
when multiplied by 2, gives an answer of 6. In this case,

2 x 3 = 6; therefore, the number is 3.

• To complete the equivalent fraction, multiply the 3 by the numerator of the
original fraction ( ). Therefore,

the equivalent fraction of is
.

• Another way to look at this:

• Repeat the process to obtain the equivalent fraction for
.

**Step 3: Now add the numerators of the equivalent fractions and retain the
common
denominator.**

**The correct answer is **