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# Pre-Algebra - Monomials

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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 2x2. 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: 2x2 and 5x4

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, x4 has the highest exponent. This then tells us that the LCM of 2x2 and 5x4 is 10x4.

1.
For the monomials given below, find the LCM.

3x5, 6x3
18x5
18x15
24x5
12x5
3: 3 x 1 = 3; 3 x 2 = 6; 3 x 3 = 9; 3 x 4 = 12
6: 6 x 1 = 6; 6 x 2 = 12
x5 has the highest exponents
LCM is 12x5
2.
For the monomials given below, find the LCM.

2x9, 4x6
8x9
4x15
4x9
8x54
2: 2 x 1 = 2; 2 x 2 = 4
4: 4 x 1 = 4
x9 has the highest exponents
LCM is 4x9
3.
For the monomials given below, find the LCM.

11x4, 9x10
20x14
99x40
99x10
99x6
11: 11 x 1 = 11; 11 x 2 = 22; 11 x 3 = 33; 11 x 4 = 44; 11 x 5 = 55; 11 x 6 = 66; 11 x 7 = 77; 11 x 8 = 88; 11 x 9 = 99
9: 9 x 1 = 9; 9 x 2 = 18; 9 x 3 = 27; 9 x 4 = 36; 9 x 5 = 45; 9 x 6 = 54; 9 x 7 = 63; 9 x 8 = 72; 9 x 9 = 81; 9 x 10 = 90; 9 x 11 = 99
x10 has the highest exponents
LCM is 99x10
4.
For the monomials given below, find the LCM.

6x2, 5x3
30x6
30x3
30x5
30x2
6: 6 x 1 = 6; 6 x 2 = 12; 6 x 3 = 18; 6 x 4 = 24; 6 x 5 = 30
5: 5 x 1 = 5; 5 x 2 = 10; 5 x 3 = 15; 5 x 4 = 20; 5 x 5 = 25; 5 x 6 = 30
x3 has the highest exponents
LCM is 30x3
5.
For the monomials given below, find the LCM.

7x7, 3x8
21x7
21x8
21x15
21x56
7: 7 x 1 = 7; 7 x 2 = 14; 7 x 3 = 21
3: 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 = 21
x8 has the highest exponents
LCM is 21x8
6.
For the monomials given below, find the LCM.

5x4, 8x7
40x7
13x7
13x28
40x11
5: 5 x 1 = 5; 5 x 2 = 10; 5 x 3 = 15; 5 x 4 = 20; 5 x 5 = 25; 5 x 6 = 30; 5 x 7 = 35; 5 x 8 = 40
8: 8 x 1 = 8; 8 x 2 = 16; 8 x 3 = 24; 8 x 4 = 32; 8 x 5 = 40
x7 has the highest exponents
LCM is 40x7
7.
For the monomials given below, find the LCM.

4x2, 6>x2
24x2
12x4
12x2
24x4
4: 4 x 1 = 4; 4 x 2 = 8; 4 x 3 = 12
6: 6 x 1 = 6; 6 x 2 = 12
Both variables have the same exponent of x2 so the LCM is 12x2
8.
For the monomials given below, find the LCM.

7x3, 9x2
63x2
63x3
63x6
63x1
7: 7 x 1 = 7; 7 x 2 = 14; 7 x 3 = 21; 7 x 4 = 28; 7 x 5 = 35; 7 x 6 = 42; 7 x 7 = 49; 7 x 8 = 56; 7 x 9 = 63
9: 9 x 1 = 9; 9 x 2 = 18; 9 x 3 = 27; 9 x 4 = 36; 9 x 5 = 45; 9 x 6 = 54; 9 x 7 = 63
x3 has the highest exponents
LCM is 63x3
9.
For the monomials given below, find the LCM.

13x5, 5x2
65x5
18x7
65x10
8x5
13: 13 x 1 = 13; 13 x 2 = 26; 13 x 3 = 39; 13 x 4 = 52; 13 x 5 = 65
5: 5 x 1 = 5; 5 x 2 = 10; 5 x 3 = 15; 5 x 4 = 20; 5 x 5 = 25; 5 x 6 = 30; 5 x 7 = 35; 5 x 8 = 40; 5 x 9 = 45; 5 x 10 = 50; 5 x 11 = 55; 5 x 12 = 60; 5 x 13 = 65
x5 has the highest exponents
LCM is 65x5
10.
For the monomials given below, find the LCM.

10x8, 2x4
20x8
20x32
8x8
10x8
10: 10 x 1 = 10
2: 2 x 1 = 2; 2 x 2 = 4; 2 x 3 = 6; 2 x 4 = 8; 2 x 5 = 10
x8 has the highest exponents
LCM is 10x8