# ACT Math : How to find the lowest / least common denominator

## Example Questions

### Example Question #1 : Lowest Common Denominator

What is the difference between the LCM and GCF for the following set of numbers:  3, 12, and 30?

Possible Answers:

48

57

60

75

None of the answers are correct

Correct answer:

57

Explanation:

LCM = least common multiple = 2 x 2 x 3 x 5 = 60

GCF = greatest common factor = 3

Prime factor each number

3 = 3 x 1

12 = 3 x 4 = 3 x 2 x 2

30 = 5 x 6 = 5 x 2 x 3

LCM – GCF = 60 – 3 = 57

### Example Question #1 : How To Find The Lowest / Least Common Denominator

What is the least common denominator of , , and ?

Possible Answers:

32

48

24

16

Correct answer:

16

Explanation:

In order to find the least common denominator, you must find the least common multiple of all three numbers.  For this problem, the least common multiple of all three numbers is 16 (divisible by 2, 4, 8 , 1, and 16).

### Example Question #491 : Arithmetic

What is the lowest common denominator for the following five fractions?

Possible Answers:

6

12

3

18

36

Correct answer:

36

Explanation:

The lowest common denominator looks at the denominator (bottom number) of all of the fractions and finds the smallest number that all of the numbers divide into.

Of those numbers the largest is 18.  First check to see if all the numbers divide into 18.  3 and 6 do, but 4 and 12 do not.  Multiply 18 by 2 and get 36.  Check to see if all the numbers divide into 36.  3 and 6 still do.  4 and 12 do now. therefore. 36 is the lowest common denominator.

### Example Question #501 : Arithmetic

Find the lowest common denominator of these four fractions:

Possible Answers:

60

24

30

45

15

Correct answer:

60

Explanation:

All of the denominators must be able to divide into the same number. First, see if the three smaller numbers (3, 4, 12) divide into the largest number (15)—NO. Then check the multiples of the largest number to see if the lower numbers divide into it:

15 * 2 = 30 (NO)

15 * 3 = 45 (NO)

15 * 4 = 60 (YES!)

### Example Question #2 : Lowest Common Denominator

Solve the following:

Possible Answers:

Correct answer:

Explanation:

Finding the common denomenator of  yields a result of

### Example Question #1 : How To Find The Lowest / Least Common Denominator

Find the least common denominator for the following fractions:

Possible Answers:

120

60

36

360

30

Correct answer:

60

Explanation:

The least common multiple of 3, 10, and 12 is 60. 60 is divisible by all three numbers (60/3 = 20, 60/10 = 6, and 60/12 = 5). Therefore, you could convert these fractions to 20/60, 25/60, and 42/60.