### All ACT Math Resources

## Example Questions

### Example Question #1 : Least Common Multiple

What is the least common multiple of 4 and 6?

**Possible Answers:**

20

12

10

24

16

**Correct answer:**

12

12 is the least common multiple of 4 and 6.

### Example Question #2 : Least Common Multiple

What is the least common multiple of 8, 25, and 40?

**Possible Answers:**

**Correct answer:**

Find the multiples of 40, and find the smallest one that is divisible by 8 and 25.

### Example Question #3 : Least Common Multiple

If *ab < *96 and *b* is a multiple of 4, what is the greatest possible value of *a*?

**Possible Answers:**

23.5

12

24

6

**Correct answer:**

24

Since we want *a* to be as large as possible, we want *b* to be as small as possible. The lowest possible value of *b*, then, is 4. If *b* is 4, then we can solve for *a* by setting up the equation:

4(a) = 96

96/4 = 24

### Example Question #4 : Least Common Multiple

What is the least common multiple of 20, 16, and 32?

**Possible Answers:**

320

4

5

160

**Correct answer:**

160

The least comon multiple is the lowest multiple of all three numbers. 160 is 32x5, 16x10, and 8x20.

### Example Question #5 : Least Common Multiple

What is the least common multiple of and ?

**Possible Answers:**

There is no least common multiple becaues both numbers are prime.

**Correct answer:**

To find the least common multiple of two numbers, if they are both prime, simply multiply the numbers.

Thus we get that

We could also write out the multiples of each number and see what numbers they have in common. The least common multiple will be the common number that appears first in both sets.

### Example Question #6 : Least Common Multiple

What is the least common multiple of

**Possible Answers:**

**Correct answer:**

To find the lowest common multiply, we need to find the smallest value which is a factor of each of the three numbers. We know it has to be even from the factor of two. If we look at the value , the lowest multiple of that number is Since the other two values are also divisible by this number, that is the lowest common multiple.

### Example Question #7 : Least Common Multiple

A sliced cake can be equally split among 4, 5, or 6 people, with each person receiving the same number of slices. Which of the following answers represents a possible number of slices that the cake could have?

**Possible Answers:**

30

120

116

56

24

**Correct answer:**

120

If you divide the answer choices by 4, 5, and 6, 120 is the only choice that divides evenly by all three numbers.

### Example Question #1 : Greatest Common Factor

What is the greatest common factor of 49, 91, and 119?

**Possible Answers:**

7

3

9

1

**Correct answer:**

7

The greatest common factor is the largest integer that divides without remainder into a set of integers. In this case, 1 and 7 are both common factors, but 7 is the *greatest* common factor.

### Example Question #2 : Greatest Common Factor

What is the greatest common factor of 55, 165, and 220?

**Possible Answers:**

5

55

20

11

**Correct answer:**

55

The greatest common factor is the largest factor that the given numbers have in common. 5 is a common factor, but it is not the greatest one; 11 and 20 are not common factors to the given numbers; however, 55 is a common factor of the given three numbers and is the greatest one at that.

### Example Question #3 : Greatest Common Factor

What is the greatest common factor of 30, 90, and 120?

**Possible Answers:**

25

3

10

30

15

**Correct answer:**

30

The greatest common factor can most easily be found by plugging in answers from your answer choices, a good strategy with these types of problems is to simply guess and check using your largest answer, in this case, we see that 30 is immediately the GCF for these three numbers

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