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

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #2 : General Fractions

3/5 + 4/7 – 1/3 =

Possible Answers:

7/9

3/37

72/89

88/105

4/3

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 #3 : General Fractions

3/5 + 4/7 – 1/3 = 

Possible Answers:

7/9

4/3

88/105

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 #4 : General Fractions

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : General Fractions

Simplify:

Possible Answers:

Correct answer:

Explanation:

First, find the common denominator of the fractions in order to add them together. Looking at the first two fractions, we can see that the common denominator is 15 because 3 times five is 15. We can now change both fractions to have a denominator of 15 so that we can add them together:

Now, find a common denominator for the remaining fractions. This can be done by listing multiples of 15 and 20 and finding the lowest common multiple:

15: 15, 30, 45, 60, 75

20: 20, 40, 60, 80

60 is the lowest common multiple, so it is our least common denominator.

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