### All ACT Math Resources

## Example Questions

### Example Question #1 : Factors / Multiples

What is the least common multiple of 4 and 6?

**Possible Answers:**

10

20

12

16

24

**Correct answer:**

12

12 is the least common multiple of 4 and 6.

### Example Question #1 : Factors / Multiples

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 #1 : Least Common Multiple

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

**Possible Answers:**

24

12

6

23.5

**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 #1 : Factors / Multiples

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

**Possible Answers:**

4

5

160

320

**Correct answer:**

160

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

### Example Question #1 : Factors / Multiples

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 #2 : Factors / Multiples

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 #1 : How To Find The 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:**

56

116

24

120

30

**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.