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As you have most likely come to learn by now, Algebra comes with a lot of different and interesting terminologies such as monomial, polynomial, variables and coefficients. In this quiz, we are going to focus on monomials and, more specifically, how to find the least common multiple (LCM) of monomials.

As a quick refresher, a **monomial is a polynomial that has only one term**. An example of a monomial would be 2*x*^{2}. It is only one term or factor on its own, as well as in a problem. [Note that the “** x**” is a variable.]

Now let’s list two monomials: **2***x*^{2} and **5***x*^{4}

The task is to now find the LCM of these two monomials. So let’s look at the coefficients (or known numbers), i.e., “**2**” and “**5**.” We then will need to multiply each of these numbers beginning by 1, then 2, then 3, etc. until we find the first common multiple number sum. This is done as follows:

**2**: 2, 4, 6, 8, **10** (To find the multiples it is: 2 x 1= 2; 2 x 2 = 4; 2 x 3 = 6; 2 x 4 = 8; 2 x 5 = 10)

**5**: 5, **10** (To find the multiples it is: 5 x 1= 5; 5 x 2 = 10)

**10** is the first least common multiple (LCM) sum of “2” and “5”.

When you have variables, the variable with the highest exponent is used as the least common multiple. In our two monomials, *x*^{4} has the highest exponent. This then tells us that the LCM of 2*x*^{2} and 5*x*^{4} is **10 x**

1.

For the monomials given below, find the LCM.

7*x*^{7}, 3*x*^{8}

7

21*x*^{7}

21*x*^{8}

21*x*^{15}

21*x*^{56}

2.

For the monomials given below, find the LCM.

3*x*^{5}, 6*x*^{3}

3

18*x*^{5}

18*x*^{15}

24*x*^{5}

12*x*^{5}

LCM is 12

Answer (d) is the correct answer

3.

For the monomials given below, find the LCM.

6*x*^{2}, 5*x*^{3}

6

30*x*^{6}

30*x*^{3}

30*x*^{5}

30*x*^{2}

LCM is 30

Answer (b) is the correct answer

4.

For the monomials given below, find the LCM.

11*x*^{4}, 9*x*^{10}

11

20*x*^{14}

99*x*^{40}

99*x*^{10}

99*x*^{6}

LCM is 99

Answer (c) is the correct answer

5.

For the monomials given below, find the LCM.

13*x*^{5}, 5*x*^{2}

13

65*x*^{5}

18*x*^{7}

65*x*^{10}

8*x*^{5}

LCM is 65

Answer (a) is the correct answer

6.

For the monomials given below, find the LCM.

2*x*^{9}, 4*x*^{6}

2

8*x*^{9}

4*x*^{15}

4*x*^{9}

8*x*^{54}

LCM is 4

Answer (c) is the correct answer

7.

For the monomials given below, find the LCM.

4*x*^{2}, 6>*x*^{2}

4

24*x*^{2}

12*x*^{4}

12*x*^{2}

24*x*^{4}

Both variables have the same exponent of

Answer (c) is the correct answer

8.

For the monomials given below, find the LCM.

5*x*^{4}, 8*x*^{7}

5

40*x*^{7}

13*x*^{7}

13*x*^{28}

40*x*^{11}

LCM is 40

Answer (a) is the correct answer

9.

For the monomials given below, find the LCM.

7*x*^{3}, 9*x*^{2}

7

63*x*^{2}

63*x*^{3}

63*x*^{6}

63*x*^{1}

LCM is 63

Answer (b) is the correct answer

10.

For the monomials given below, find the LCM.

10*x*^{8}, 2*x*^{4}

10

20*x*^{8}

20*x*^{32}

8*x*^{8}

10*x*^{8}

LCM is 10

Answer (d) is the correct answer

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7:7 x 1 = 7; 7 x 2 = 14; 7 x 3 =213:3 x 1 = 3; 3 x 2 = 6; 3 x 3 = 9; 3 x 4 = 12; 3 x 5 = 15; 3 x 6 = 18; 3 x 7 =21x^{8}has the highest exponentsLCM is 21

x^{8}Answer (b) is the correct answer