LCM GCF Ladder

Multiple Choice

What is the prime factorization of 36?

(Draw a factor tree on your paper. List all the prime numbers at the ends of the branches as a multiplication sentence.)

• 2 * 3

• 2 * 2 * 3 * 3

• 2 * 2 * 3

• 3 * 3 * 3 * 2

Multiple Choice

What is the prime factorization of 100?

(Draw a factor tree on your paper. List all the prime numbers at the ends of the branches as a multiplication sentence.)

• 5 * 2

• 2 * 2 * 5

• 2 * 2 * 5 * 5

• 5 * 2 * 2 * 2

Dropdown

Draw a Venn Diagram on your paper like this one.

Using your factor trees, list the SHARED multiples of 36 and 100.

The shared factors are ​​​

Select answer

and ​

Select answer

. This means that the GCF is the product of those factors, or ​

Select answer

.

Multiple Choice

What is the GCF (greatest common factor) of 21 and 84?

On your paper, show the factor trees for each AND a Venn Diagram.

• 3

• 21

• 7

• 42

• 6

Multiple Choice

Which of the following is equivalent to 30 + 50?

Show your work on your paper.

• 10(30+50)

• 10(3+5)

• 5(6+9)

• 5(5+10)

• 10(20+30)

Multiple Choice

What is the GCF (greatest common factor) of 60 and 48?

On your paper, show the factor trees for each AND a Venn Diagram.

• 2

• 10

• 12

• 6

• 4

Labelling

Create the correct distributive property expression for 60 - 48 by factoring out the GCF from the last question.

Hint: Write down the correct answer on your paper. Start with the GCF outside the parenthesis.

Drag labels to their correct position on the image

6

5

4

12

10

8

Multiple Choice

What is the GCF (greatest common factor) of 18 and 24?

On your paper, show the factor trees for each AND a Venn Diagram.

• 2

• 10

• 12

• 6

• 3

Labelling

Create the correct distributive property expression for 18 + 24 by factoring out the GCF from the last question.

Hint: Write down the correct answer on your paper. Start with the GCF outside the parenthesis.

Drag labels to their correct position on the image

2

4

12

8

3

6

Math Response

What is the LCM (Least Common Multiple) of 4 and 10?

On your paper, list the multiples of 4 and 10 until you find the match.

Type answer here

Correct Answer: 20

Deg^°

Rad

Multiple Choice

Is this a correct answer?

This does NOT have to go on your paper.

• Yes, the student correctly added.
• No, you cannot add unlike denominators
• No, 5 + 7 is not 12
• No, 2 + 3 is not 5

Multiple Choice

$$\frac{1}{2}$$  +  $$\frac{2}{5}$$  =

On your paper, demonstrate finding the least common multiple for the denominator and rewriting the fractions to add them.

• $$\frac{9}{10}$$  

• $$\frac{3}{7}$$  

• $$\frac{1}{3}$$  

• $$\frac{9}{20}$$  

Math Response

Mr. Brewer and Mr. Cowden were eating pizza. Mr. Brewer ate $$\frac{3}{12}$$   of the pizza. Mr. Cowden ate  $$\frac{3}{6}$$   of the pizza. What fraction of the pizza was NOT eaten?

On your paper, show the work.

Type answer here

Correct Answer: \frac{1}{4}

Deg^°

Rad

Multiple Choice

What would be the EXPANDED prime factorization of the number 18?

• 2 x 3 x 3

• 3 x 6

• 2 x 9

• 2 x 3

Multiple Choice

What would be the prime factorization of the number 75?

• 5 x 5 x 5

• 3 x 3 x 5

• 3² x 5

• 3 x 5²

Multiple Choice

Find the GCF of:

• 1

• 15

• 115

• 345

Multiple Choice

Which answer would represent the GCF and Distributive Property of the numbers pictured?

• 12 ( 2 + 1 )

• 6 ( 2 + 1 )

• 6 ( 4 + 2 )

• 4 ( 6 + 3 )

Multiple Choice

Find the GCF:

• 5

• 1

• 30

• 10

Multiple Choice

Find the GCF:

• 1

• 2

• 8

• 12

Multiple Choice

Answer the following question by finding the GCF.

• 18

• 9

• 12

• 1

Multiple Choice

Find the LCM of:

• 1

• 5

• 10

• 20

Multiple Choice

Find the LCM of:

• 60

• 1

• 30

• 3

Multiple Choice

Which answer would represent the GCF and Distributive Property of the numbers pictured?

• 1 ( 9 + 21 )

• 9 ( 1 + 3 )

• 3 ( 3 + 7 )

• 3 ( 3 + 9 )

Multiple Choice

Answer the following question by finding the LCM.

• 90 minutes

• 30 minutes

• 1:45pm

• 1:00pm

Multiple Choice

Is 49 prime or composite?

• Prime

• Composite

Multiple Choice

Is 63 prime or composite?

• Prime

• Composite

Multiple Choice

Is 37 prime or composite?

• Prime

• Composite

Multiple Choice

What is the expanded prime factorization of 36?

• 2 x 18

• 2 x 2 x 3 x 3

• 2 x 2 x 9

• 2 x 2 x 2 x 3

Multiple Choice

What is the standard prime factorization of 18?

• $$2\ x\ 3^2$$  

• $$2\times9$$  

• $$2^2\times3$$  

• $$3\times6$$   

Multiple Choice

Tommy has 24 football cards and 40 baseball cards. What is the greatest number of friends Tommy could equally split his cards between?

• 8 friends

• 4 friends

• 2 friends

• 12 friends

Multiple Choice

What is the GCF of 7 and 15?

• 2

• 1

• 7

• 60

Multiple Choice

Every 4th student in the lunch line gets a free milk, and every 6th student in the lunch line gets a free fruit. What student would be the first to receive a free milk and fruit?

• 4th student

• 6th student

• 12th student

• 24th student

Multiple Choice

Find the LCM of 10 and 12.

• 2

• 20

• 1

• 60

Multiple Choice

What is the greatest common factor (GCF) of 20 and 30?

• 60

• 5

• 10

• 30

Multiple Choice

What is the greatest common factor (GCF) of 24 and 30?

• 2

• 12

• 6

• 3

Multiple Choice

What is the greatest common factor (GCF) of 18 and 24?

• 3

• 6

• 8

• 9

Multiple Choice

Find the least common multiple (LCM) of 9 and 5.

• 5

• 9

• 45

• 36

Multiple Choice

What is the least common multiple (LCM) of 3 and 20?

• 60
• 40
• 20
• 3

Multiple Choice

Use a factor tree to find the prime factorization of 18

• 3x2x2

• 3x3x3

• 33x3

• 3x3x2

Multiple Choice

Using a factor tree, to find the prime factorization of

48

• 12x2x2

• 6x8

• 8x3x2

• 3x2x2x2x2

Multiple Choice

Rewrite using distributive property and GCF. 24+30

• 6(4+5)

• 8(3+4)

• 6(4) + 6(2)

• 6x2+5

Multiple Choice

Rewrite using distributive property and GCF. 35+21

• 49(5+3)

• 7(5+3)

• 7(28+14)

• 49(28+14)

Multiple Choice

Find the greatest common factor (GCF) of 21 and 28

• 3

• 4

• 7

• 14

Multiple Choice

What is the LCM for 4 and 7?

• 4
• 7
• 14
• 28

Multiple Choice

What is the LCM for 3 and 9?

• 3
• 9
• 27
• 18

Multiple Choice

What is the LCM for 5 and 8?

• 5
• 8
• 20
• 40

Multiple Choice

What is the GCF of 18 and 24?

• 3

• 6

• 8

• 9

Multiple Choice

What is the GCF of 4 and 12?

• 3
• 1
• 6
• 4

Multiple Choice

What is the greatest factor of 28 and 49?

• 1
• 2
• 7
• 12

Multiple Choice

Which is the prime factorization of 12 ? 

• 2 x 6
• 2 + 2 + 2 + 2 + 2 + 2 
• 2² x 3
• 1 x 2² x 3

Multiple Choice

What is the prime factorization of 16 ? 

• 1 x 16
• 2²x 4
• 2⁴
• 2² + 2²

Multiple Choice

Find the prime factorization of 72

• 2³ x 3²

• 2 x 3² x 4

• 2⁴ x 3³

• 2² x 6²

Multiple Choice

Rewrite using distributive property and GCF.  
24 + 30

• 6(4+5)
• 8(3+4)
• 6(4) + 6(2)
• 6x2+5

Multiple Choice

8(3 + 4) =

• 24 + 32
• 11 + 12
• 123 + 124
• 5 + 4

Multiple Choice

Factor this expression using GCF:
36 + 24

• 2 (18 + 12)
• 3 (12 + 8)
• 6(6 + 4)
• 12 ( 3 + 2)

Multiple Choice

8(3 + 4) =

• 24 + 32
• 11 + 12
• 123 + 124
• 5 + 4

Multiple Choice

6

• Prime

• Composite

Multiple Choice

17

• Prime

• Composite

Multiple Choice

21

• Prime

• Composite

Multiple Choice

65

• Prime

• Composite

Multiple Choice

What is the LCM of 2 and 14?

• 28

• 7

• 14

• 2

Match

Match the following

• 35 + 28

• 56 + 42

• 14 + 77

• 27 + 12

• 18 + 36

7 (5 + 4)

7 (8 + 6)

7 (2 + 11)

3 (9 + 4)

6 (3 + 6)

• 7 (5 + 4)

• 7 (8 + 6)

• 7 (2 + 11)

• 3 (9 + 4)

• 6 (3 + 6)

Drag and Drop

8 x 12 = 8 (​

Placeholder

+10)

Drag these tiles and drop them in the correct blank above

2

12

16

10

80

96

Labelling

What numbers are missing in the factor tree?

Drag labels to their correct position on the image

6

9

3

5

2

Multiple Choice

Find the equivalent expression.

9 x 9 x 9 x 9 x 9

• 9⁵
• 9¹⁵
• 9 x 5
• 9 + 9 + 9 + 9+ 9

Multiple Choice

Choose the answer.
5²

• 10
• 15
• 20
• 25

Multiple Choice

GCF of 18 and 24

• 2
• 3
• 4
• 6

Multiple Choice

What is the least common multiple (LCM) of 5 and 20?

• 4
• 5
• 20
• 100

Multiple Choice

What is the least common multiple (LCM) of 4 and 10?

• 4
• 40
• 15
• 20

Multiple Choice

What is the least common multiple (LCM) of 6 and 8?

• 6
• 8
• 48
• 24

Multiple Choice

35 + 40 = 5(7 + ___)

• 5

• 6

• 7

• 8

Multiple Choice

Using distributive property and GCF find an equivalent expression for:

24 + 30

• 6(4+5)

• 8(3+4)

• 6(4) + 6(2)

• 6x2+5

Multiple Choice

GCF of 24 and 56

• 2
• 4
• 6
• 8

Multiple Choice

Using the Distributive Property, find an equivalent expression for:

8(3 + 4) =

• 24 + 32

• 11 + 12

• 123 + 124

• 5 + 4

Fill in the Blanks

Fill in the Blanks

Multiple Select

Which expressions are equal to the sum of 21 + 49? Choose ALL that apply.

• 7(4 + 7)

• 7(3 + 7)

• 2(7 + 17)

• (7 + 3) + (7 + 7)

• (7 x 3) + (7 x 7)

Multiple Choice

How can 5(3 +2) be expressed using the distributive property?

• 5(3) x 5(2)

• (5 x 3) x (5 x 2)

• 5(3) + 5(2)

• (5 + 3) x (5+2)

Multiple Select

Monica uses the distributive property to write an equivalent expression to 32 + 40.

Which expression did Monica write?

• 8(4 + 5)

• 4(16 + 10)

• 8(26 + 32)

• 4(8 + 10)

Multiple Choice

Sonia is solving the problem 3(4 + 6) using an area model.

Which area model correctly solves Sonia's problem?

Multiple Choice

Rewrite the numeric expression using the Distributive Property and the GCF (greatest common factor).

36 + 60

• 6 (7 + 10)

• 12 (3 + 5)

• 18 (2 + 10)

• 24 (1 + 2)

Topic 3 Review Order of Operations, Prime Factors, GCF, and LCM

by Karen Martin

Multiple Choice

$$3^3\ =$$  

• 9

• 27

• 18

• 81

Multiple Choice

$$25^0\ =$$  

• 25

• 0

• 1

• 250

Multiple Choice

$$5^2\ =$$  

• 10

• 5

• 20

• 25

Multiple Choice

$$4^2\ \ \ \ \ \ \ \ \ \ 2^4$$  

• <

• >

• =

​Remember anything to the zero power = 1

​And anything to the power of one = itself

Multiple Choice

$$72^0\ \ \ \ \ \ \ \ \ \ \ 45^{1\ \ \ \ \ }$$  

• <

• >

• =

Multiple Choice

$$5^2\ \ \ \ \ \ \ \ \ \ 2^3$$  

• <

• >

• =

​Use factor trees to find the prime factorization of a number.

​

​36 = 2 • 2 • 3 • 3

​or

​36 = 2² • 3²

Multiple Choice

What is the prime factorization of 84?

• 2 • 2 • 3 • 7

• 4 • 21

• 2 • 3 • 7

• 2 • 6 • 7

Multiple Choice

What is the prime factorization of 45?

• 1 • 3 • 3 • 5

• 9 • 5

• 3 • 3 • 5

• 3 • 15

​Use division ladders to find the GCF and LCM

​

GCF = greatest common factor

​the biggest number that can divide

into them evenly

​

LCM = least common multiple

​The smallest number that is a multiple

​of the numbers. The original numbers

​are factors of the LCM.

Multiple Choice

Find the GCF of 48 and 60.

• 4

• 12

• 6

• 22

Multiple Choice

Find the GCF of 81 and 54.

• 27

• 3

• 9

• 18

​Factor out the GCF with the Distributive Property

Multiple Choice

Use GCF and the Distributive Property to find the sum of 81 + 18

• 3(9 + 6)

• 18(7 + 1)

• 9(9 +2)

Multiple Choice

Use GCF and the Distributive Property to find the sum of 44 + 77

• 11(4 + 7)

• 4 + 7(11)

• 11(4 +3)

Multiple Choice

Find the LCM of 6 and 21

• 21

• 126

• 42

• 3

Multiple Choice

Find the LCM of 15 and 20.

• 5

• 60

• 300

• 30

​Follow the Order of Operations

24 + t

​

j - 4​

The total of 24 plus t

​

4 less than j​

Variables can be used for unknown numbers in expressions.

Pay attention to the order you write the numbers and variables. It matters!

The product of h and 18

18h

​

72 shared with k groups

72 ÷ k​

Pay attention to the order you write the numbers and variables. It matters!

Multiple Choice

15 fewer than m

• 15 - m

• m - 15

• 15m

• 15 + m

Multiple Choice

The sum of a number k and 12

• k + 12

• k - 12

• 12k

• $$\frac{12}{k}$$  

Multiple Select

The quotient of b and 10

Mark all correct answers.

• $$b\div10$$  

• $$\frac{10}{b}$$  

• 10b

• $$\frac{b}{10}$$  

Multiple Choice

The product of c and 27

• c + 27

•  27 + c

• 27c

• $$\frac{c}{27}$$  

Multiple Choice

9 more than 5 times the number p

• $$\left(\frac{p}{5}\right)\ +\ 9$$  

• 9 + 5 + p

• 9(5 + p)

•  9 + 5p

Multiple Choice

three times j plus 7

• $$\left(\frac{3}{j}\right)\ +\ 7$$  

• 3j + 7

• 3 + j + 7

• 3(j + 7)

Please practice more on your own. Use your notes. Good Luck!