Study Island
Copyright © 2015 Edmentum - All rights reserved.
Generation Date: 02/22/2015
Generated By: Robert Dilliplane
1. Look at the two monomials below.
36xy3
20xy4
What is the least common multiple (LCM) of the monomials shown above?
A. 4x2y7
B. 4xy3
C. 180x2y7
D. 180xy4
2.
7xy2
14x3y3
7x2y4
What is the greatest common factor (GCF) of the monomials shown above?
A. 14x3y4
B. 7x3y4
C. 7xy2
D. 14x6y9
3. Look at the three monomials below.
18xy3z
30x2y3z4
10xy2
What is the least common multiple (LCM) of the monomials shown above?
A. 90x3y6z5
B. 6xy3z
C. 6xy3
D. 90x2y3z4
4. Look at the two monomials below.
6x4y4
10x2yz2
What is the least common multiple (LCM) of the monomials shown above?
A. 30x6y5z2
B. 30x4y4z2
C. 2x2yz
D. 2x2y
5.
42x2y2z4
30x4y
What is the greatest common factor (GCF) of the monomials shown above?
A. 210x6y3z4
B. 6x4y2z4
C. 210x4y2z4
D. 6x2y
6. Look at the two monomials below.
36xy3z
20xyz4
What is the least common multiple (LCM) of the monomials shown above?
A. 4x2y4z5
B. 180x2y4z5
C. 4xyz
D. 180xy3z4
7.
78u4v2w2
30u2v3w3
What is the greatest common factor (GCF) of the monomials shown above?
A. 390u6v5w5
B. 6u2v2w2
C. 6u4v3w3
D. 390u2v2w2
8.
14xy
10x3y2
What is the greatest common factor (GCF) of the monomials shown above?
A. 70x3y2
B. 70x4y3
C. 2xy
D. 2x3y2
9.
91x2yz4
14x3y2z3
What is the greatest common factor (GCF) of the monomials shown above?
A. 182x5y3z7
B. 182x3y2z4
C. 7x3y2z4
D. 7x2yz3
10. Look at the two monomials below.
54u2v2w
30u2v4w4
What is the least common multiple (LCM) of the monomials shown above?
A. 6u2v2w
B. 270u4v6w5
C. 270u2v4w4
D. 6u4v6w5
Answers
1. D
2. C
3. D
4. B
5. D
6. D
7. B
8. C
9. D
10. C
Explanations
1. Find the least common multiple (LCM) of the monomials by finding the LCM of the constants
and of each of the variables.
The LCM of 36 and 20 is 180.
The LCM of x and x is x.
The LCM of y3 and y4 is y4.
Therefore, the LCM of the two monomials is 180xy4.
2. Find the greatest common factor (GCF) of the monomials by finding the GCF of the constants
and of each of the variables.
The GCF of 7, 14, and 7 is 7.
The GCF of x, x3, and x2 is x.
The GCF of y2, y3, and y4 is y2.
Therefore, the GCF of the three monomials is 7xy2.
3. Find the least common multiple (LCM) of the monomials by finding the LCM of the constants
and of each of the variables.
The LCM of 18, 30, and 10 is 90.
The LCM of x, x2, and x is x2.
The LCM of y3, y3, and y2 is y3.
The LCM of z, z4, and is z4.
Therefore, the LCM of the three monomials is 90x2y3z4.
4. Find the least common multiple (LCM) of the monomials by finding the LCM of the constants
and of each of the variables.
The LCM of 6 and 10 is 30.
The LCM of x4 and x2 is x4.
The LCM of y4 and y is y4.
The LCM of z0 (z0 = 1) and z2 is z2.
Therefore, the LCM of the two monomials is 30x4y4z2.
5. Find the greatest common factor (GCF) of the monomials by finding the GCF of the constants
and of each of the variables.
The GCF of 42 and 30 is 6.
The GCF of x2 and x4 is x2.
The GCF of y2 and y is y.
The GCF of z4 and z0 (z0 = 1) is z0 = 1.
Therefore, the GCF of the two monomials is 6x2y.
6. Find the least common multiple (LCM) of the monomials by finding the LCM of the constants
and of each of the variables.
The LCM of 36 and 20 is 180.
The LCM of x and x is x.
The LCM of y3 and y is y3.
The LCM of z and z4 is z4.
Therefore, the LCM of the two monomials is 180xy3z4.
7. Find the greatest common factor (GCF) of the monomials by finding the GCF of the constants
and of each of the variables.
The GCF of 78 and 30 is 6.
The GCF of u4 and u2 is u2.
The GCF of v2 and v3 is v2.
The GCF of w2 and w3 is w2.
Therefore, the GCF of the two monomials is 6u2v2w2.
8. Find the greatest common factor (GCF) of the monomials by finding the GCF of the constants
and of each of the variables.
The GCF of 14 and 10 is 2.
The GCF of x and x3 is x.
The GCF of y and y2 is y.
Therefore, the GCF of the two monomials is 2xy.
9. Find the greatest common factor (GCF) of the monomials by finding the GCF of the constants
and of each of the variables.
The GCF of 91 and 14 is 7.
The GCF of x2 and x3 is x2.
The GCF of y and y2 is y.
The GCF of z4 and z3 is z3.
Therefore, the GCF of the two monomials is 7x2yz3.
10. Find the least common multiple (LCM) of the monomials by finding the LCM of the
constants and of each of the variables.
The LCM of 54 and 30 is 270.
The LCM of u2 and u2 is u2.
The LCM of v2 and v4 is v4.
The LCM of w and w4 is w4.
Therefore, the LCM of the two monomials is 270u2v4w4.