What is the Lowest Common Denominator?
You will need to find the lowest common denominator, sometimes called the LCD, in order to do most problems on fractions.
Finding the lowest common denominator means that you need to express all of the fractions with the same number on the bottom.
You may need to find the lowest common denominator in order to add or subtract fractions.
However, you will not need to find the lowest common denominator if you are multiplying or dividing fractions.
Have a look at the following problems.
Adding Fractions − Lowest Common Denominator
\(\frac{4}{9} + \frac{2}{27} = ? \)
We cannot easily add the two fractions together since they do not have the same denominators.
Solve the problem using the following steps.
STEP 1: Find the common factors of the denominators.
You have to find the common factors of 9 and 27.
Factors are numbers that equal the product when they are multiplied together.
The factors of 9 are 1, 3, and 9.
We know these are the factors of 9 because:
1 × 9 = 9
3 × 3 = 9
Then we need to find the factors of 27.
The factors of 27 are 1, 3, 9, and 27.
We know these are the factors of 27 because:
1 × 27 = 27
3 × 9 = 27
STEP 2: Find the common factors.
Now look at the factors for both denominators and see what they have in common.
Here, we can see the common factors if we highlight the numbers the expressions have in common.
1 × 9 = 9
3 × 3 = 9
1 × 27 = 27
3 × 9 = 27
So, the common factors are 3 and 9.
STEP 3: Express the fractions in the lowest common denominator.
We can see from above that we need to take 9 (the denominator of the first fraction) times 3 in order to get 27 (the denominator of the second fraction).
We multiply the numerator by 3 and the denominator by 3 in order to convert the first fraction to the lowest common denominator.
\(\frac{4}{9} + \frac{2}{27} = \)
\(\frac{4 \times 3}{9 \times 3} + \frac{2}{27} = \)
\(\frac{12}{27} + \frac{2}{27} \)
STEP 4: Finally, perform the addition to solve the problem.
\(\frac{12}{27} + \frac{2}{27} = \)
\(\frac{14}{27}\)
Subtracting Fractions − Lowest Common Denominator
Now, we will go through the steps again, this time with subtraction.
\(\frac{17}{32} – \frac{3}{8} = ? \)
STEP 1: Find the common factors of 32 and 8.
The factors of 32 are 1, 2, 4, 8, 16, and 32 because:
1 × 32 = 32
2 × 16 = 32
4 × 8 = 32
The factors of 8 are 1, 2, 4, and 8 because:
1 × 8 = 8
2 × 4 = 8
STEP 2: Find the common factors.
The common factors are 2, 4, and 8.
So. we need to multiply by 4 in order to get the LCD of 32 in the next step.
STEP 3: Express the fractions in the lowest common denominator.
\(\frac{17}{32} – \frac{3}{8} = \)
\(\frac{17}{32} – \frac{3 \times 4}{8 \times 4} = \)
\(\frac{17}{32} – \frac{12}{32} \)
STEP 4: Finally, perform the subtraction to solve the problem.
\(\frac{17}{32} – \frac{12}{32} =\)
\(\frac{5}{32}\)
Lowest Common Denominator – Exercises
Now try these exercises and check your answers.
You may need to simplify some of your fractions once you find the LCD.
\(\text{1)} \frac{5}{36} + \frac{1}{6} = ? \)
\(\text{2)} \frac{21}{24} – \frac{3}{8} = ? \)
\(\text{3)} \frac{4}{15} + \frac{3}{5} = ? \)
\(\text{4)} \frac{17}{21} – \frac{2}{3} = ? \)
\(\text{5)} \frac{5}{17} + \frac{3}{34} = ? \)
Lowest Common Denominator – Answers
\(\text{1)} \frac{5}{36} + \frac{1}{6} = ? \)
\(\frac{5}{36} + \frac{1}{6} = \)
\(\frac{5}{36} + \frac{1 \times 6}{6 \times 6} = \)
\(\frac{5}{36} + \frac{6}{36} = \)
\(\frac{11}{36}\)
\(\text{2)} \frac{21}{24} – \frac{3}{8} = ? \)
\(\frac{21}{24} – \frac{3}{8} = \)
\(\frac{21}{24} – \frac{3 \times 3}{8 \times 3} = \)
\(\frac{21}{24} – \frac{9}{24} = \)
\(\frac{12}{24} = \)
\(\frac{1}{2}\)
\(\text{3)} \frac{4}{15} + \frac{3}{5} = ? \)
\(\frac{4}{15} + \frac{3}{5} = \)
\(\frac{4}{15} + \frac{3 \times 3}{5 \times 3} = \)
\(\frac{4}{15} + \frac{9}{15} = \)
\(\frac{13}{15}\)
\(\text{4)} \frac{17}{21} – \frac{2}{3} = ? \)
\(\frac{17}{21} – \frac{2}{3} = \)
\(\frac{17}{21} – \frac{2 \times 7}{3 \times 7} = \)
\(\frac{17}{21} – \frac{14}{21} = \)
\(\frac{3}{21} = \)
\(\frac{1}{7}\)
\(\text{5)} \frac{5}{17} + \frac{3}{34} = ? \)
\(\frac{5}{17} + \frac{3}{34} = \)
\(\frac{5 \times 2}{17 \times 2} + \frac{3}{34} = \)
\(\frac{10}{34} + \frac{3}{34} = ? \)
\(\frac{13}{34}\)