LCM and GCF Homework
Multiple Choice
Identify the choice that best completes the statement or answers the question.
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1. Write the prime factorization of 54.
a. 2 • 3 • 3 • 3
c. 2 • 2 • 3 • 5
b. 2 • 2 • 3 • 4
d. 1 • 2 • 3 • 9
2. It takes 120 drops of water to fill a teaspoon. Write the prime factorization of 120 using exponents.
a. 22 • 3 • 5
c. 23 • 3 • 5
b. 2 • 3 • 5
d. 23 • 15
3. Find the GCF of 63, 72, and 24.
a. 2
c. 4
b. 6
d. 3
4. Allison works at a bakery. She must box 30 rolls, 24 muffins, and 48 biscuits so that all of the
boxes have the same number of each. What is the greatest number of boxes she can use?
a. 12 boxes
c. 6 boxes
b. 8 boxes
d. 2 boxes
5. The sixth-grade class has 12 boys and 8 girls. The teacher wants to divide them into groups that
have the same number of boys and the same number of girls. What is the greatest possible number
of groups the teacher can make?
a. 4 groups
c. 6 groups
b. 8 groups
d. 2 groups
6. A bag of hot dog buns contains 8 buns, and a package of hot dogs contains 10 hot dogs. How many
packages of each are needed so that each of the 40 campers has hot dogs and buns with none left
over?
a. 5 bags of buns, 4 packages of hot dogs c. 2 bags of buns, 2 packages of hot dogs
b. 8 bags of buns, 10 packages of hot
d. 4 bags of buns, 5 packages of hot dogs
dogs
7. Each student needs a pencil and an eraser to take a test. If pencils come 8 in a box and erasers
come 10 in a bag, what is the least number of boxes and bags needed for 40 students to each have a
pencil and an eraser?
a. 5 boxes of pencils, 4 bags of erasers
c. 2 boxes of pencils, 2 bags of erasers
b. 4 boxes of pencils, 5 bags of erasers
d. 8 boxes of pencils, 10 bags of erasers
8. Find the least common multiple (LCM) of 8 and 10.
a. 24
c. 40
b. 42
d. 30
9. Find the least common multiple (LCM) of 3, 5, and 10.
a. 51
c. 10
b. 9
d. 30
10. The difference between two numbers is 12. The LCM of the two numbers is 133. Find the two
numbers.
a. 12 and 19
c. 7 and 19
b. 19 and 31
d. 19 and 49
LCM and GCF Homework
Answer Section
MULTIPLE CHOICE
1. ANS: A
Use a factor tree. Choose any two factors of 54 to begin. Keep finding factors until each number
ends at a prime factor.
Feedback
A
B
C
D
Correct!
All the factors should be prime numbers.
Multiply the factors to check your answer.
All the factors should be prime numbers.
PTS:
OBJ:
TOP:
KEY:
2. ANS:
1
DIF: Basic
REF: Page 170
4-2.2 Writing Prime Factorizations NAT: 8.1.5.b
4-2 Factors and Prime Factorization
factor | prime factorization
C
STA: M6N1.b
120 = 23 • 3 • 5
Feedback
A
B
C
D
Check to see what the product of these numbers are.
Use an exponent if a factor occurs more than once.
Correct!
Prime factors are not divisible by anything other than themselves and 1.
PTS: 1
DIF: Advanced
NAT: 8.1.5.b
STA: M6N1.b
TOP: 4-2 Factors and Prime Factorization
3. ANS: D
List all the factors of each number, and find the factors that are common to all three. The greatest
one is the GCF.
Feedback
A
B
C
D
Find a common factor that is the greatest.
Find a factor that is shared by all three numbers.
Find a factor that is shared by all three numbers.
Correct!
PTS:
NAT:
KEY:
4. ANS:
1
DIF: Basic
REF: Page 173
OBJ: 4-3.1 Finding the GCF
8.1.5.b
STA: M6N1.c
TOP: 4-3 Greatest Common Factor
GCF | greatest common factor | factor
C
Find the GCF of the three numbers by either listing the factors, using prime factorization, or using
a ladder diagram.
Feedback
A
B
C
D
Find a factor that is shared by all three numbers.
Find a factor that is shared by all three numbers.
Correct!
Find a common factor that is the greatest.
PTS: 1
DIF: Average
REF: Page 174
OBJ: 4-3.2 Problem-Solving Application NAT: 8.1.5.b
STA: M6N1.c
TOP: 4-3 Greatest Common Factor
KEY: GCF | greatest common factor | factor | problem solving
5. ANS: A
Find the GCF of the number of boys and the number of girls by either listing the factors, using
prime factorization, or using a ladder diagram.
Feedback
A
B
C
D
Correct!
Find a factor that is shared by both numbers.
Find a factor that is shared by both numbers.
Find a common factor that is the greatest.
PTS: 1
DIF: Average
REF: Page 174
OBJ: 4-3.2 Problem-Solving Application NAT: 8.1.5.b
STA: M6N1.c
TOP: 4-3 Greatest Common Factor
KEY: GCF | greatest common factor | factor | problem solving
6. ANS: A
Find the least common multiple of the number of buns and the number of hot dogs. The LCM is
the smallest multiple of each that divides evenly into the number of campers.
Feedback
A
B
C
D
Correct!
Find the least common multiple of the number of buns and the number of hot
dogs.
Use a model to find the LCM.
You have reversed the numbers.
PTS: 1
DIF: Average
REF: Page 228
OBJ: 5-1.1 Application
NAT: 8.1.5.b
STA: M6N1.c
TOP: 5-1 Least Common Multiple
KEY: LCM | least common multiple
7. ANS: A
Find the least common multiple of the number of pencils and erasers per container. The LCM is
the smallest multiple of each that divides evenly into the number of students.
Feedback
A
B
C
D
Correct!
You have reversed the numbers.
Use a model to find the LCM.
Find the least common multiple of the number of pencils and erasers per
container.
PTS: 1
DIF: Average
REF: Page 228
OBJ: 5-1.1 Application
NAT: 8.1.5.b
STA: M6N1.c
TOP: 5-1 Least Common Multiple
KEY: LCM | least common multiple
8. ANS: C
List multiples of 8 and 10. Find the smallest number that is in both lists.
Feedback
A
B
C
D
Both numbers need to divide evenly into the multiple.
First, list multiples of the numbers. Then, find the smallest number that is in both
lists.
Correct!
Both numbers need to divide evenly into the multiple.
PTS: 1
DIF: Basic
REF: Page 229
OBJ: 5-1.2 Using Multiples to Find the LCM
NAT: 8.1.5.b
STA: M6N1.c
TOP: 5-1 Least Common Multiple
KEY: LCM | least common multiple
9. ANS: D
Write the prime factorization of each number. Identify all the common factors. Multiply all the
prime factors, using those that are common to all the numbers only once.
Feedback
A
B
C
D
All the numbers need to divide evenly into the multiple.
First, write the prime factorization of each number, and identify all the common
factors. Then, multiply all the prime factors, using those that are common to all
the numbers only once.
All the numbers need to divide evenly into the multiple.
Correct!
PTS:
OBJ:
STA:
KEY:
10. ANS:
1
DIF: Average
REF: Page 229
5-1.2 Using Multiples to Find the LCM
NAT: 8.1.5.b
M6N1.c
TOP: 5-1 Least Common Multiple
LCM | least common multiple
C
Condition 1: The difference between the numbers is given.
m − n = 12
Condition 2: The LCM is divisible by both numbers.
m • n = ? • 133
133 = 19
7
19 − 7 = 12
Find the least number that divides the LCM. Compare the quotient
to that number and see if the difference is the same as the given
difference. If not, try the next greater number that divides the LCM
and so on until both numbers satisfy both conditions.
Feedback
A
B
C
D
The difference between the two numbers is not correct.
Both numbers must divide the given number.
Correct!
The difference between the two numbers is not correct.
PTS: 1
DIF: Advanced
TOP: 5-1 Least Common Multiple
STA: M6N1.c