SAT Math : How to find the lowest / least common denominator

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Lowest Common Denominator

3/5 + 4/7 – 1/3 = 

Possible Answers:

7/9

88/105

4/3

3/37

72/89

Correct answer:

88/105

Explanation:

We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35. 

Now to the subtraction. The lowest common denominator of 35 and 3 is 35 * 3 = 105, so altogether, 3/5 + 4/7 – 1/3 = 41/35 – 1/3 = 123/105 – 35/105 = 88/105. This does not simplify and is therefore the correct answer.

Example Question #2 : Lowest Common Denominator

What is the lowest common denominator of the fractions below? 

\(\displaystyle \frac{1}{6}, \frac{4}{21}, \frac{2}{3}\)

Possible Answers:

\(\displaystyle 84\)

\(\displaystyle 42\)

\(\displaystyle 21\)

\(\displaystyle 3\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 42\)

Explanation:

In order to find the lowest common denominator, you must first list the multiples of each of the denominators of the three fractions:

\(\displaystyle 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45\)

\(\displaystyle 6: 6, 12, 18, 24, 30, 36, 42, 48\)

\(\displaystyle 21: 21, 42, 63\)

The lowest common denominator between these three sets of multiples is \(\displaystyle 42\)

Example Question #2 : How To Find The Lowest / Least Common Denominator

What is the Lowest Common Denominator of \(\displaystyle \frac{1}{6}\) ,\(\displaystyle \frac{1}{3}\)and \(\displaystyle \frac{1}{7}\)?

Possible Answers:

\(\displaystyle 126\)

\(\displaystyle 42\)

\(\displaystyle 14\)

\(\displaystyle 49\)

\(\displaystyle 9\)

Correct answer:

\(\displaystyle 42\)

Explanation:

\(\displaystyle 3:3,6,9,12,15,18,21,24,27,30,33,36,39,42\)

\(\displaystyle 6:6,12,18,24,30,36,42\)

\(\displaystyle 7:7,14,21,28,35,42\)

The smallest number they all have in common in \(\displaystyle 42\).

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