Factor Trees Probability, Ratios And Rates Worksheet Page 4
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Date
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LESSON
Factor Trees and Least Common Multiples
12 1
Journal
Ongoing Assessment:
The least common multiple of two numbers is the smallest number that is a
multiple of both numbers.
Page 394
Recognizing Student Achievement
Example:
Find the least common multiple of 8 and 12.
Problem 4
Step 1
List the multiples of 8: 8, 16, 24, 32, 40, 48, 56, and so on.
Step 2
List the multiples of 12: 12, 24, 36, 48, 60, and so on.
Use journal page 394, Problem 4 to assess students’ ability to factor numbers
Step 3
24 and 48 are in both lists. They are common multiples.
24 is the smallest number. It is the least common multiple for 8 and 12.
and identify the prime factorizations. Students are making adequate progress if
24 is also the smallest number that can be divided by both 8 and 12.
they correctly form the factor pairs in each factor tree and write the correct
Another way to find the least common multiple for two numbers is to use
prime factorization.
prime factorizations.
Example:
Find the least common multiple of 8 and 12.
[Number and Numeration Goal 3]
Step 1
Write the prime factorization of each number:
8
2 º 2 º 2
12
2 º 2 º 3
Step 2
Circle pairs of common factors. Then cross out one factor in each
pair as shown below.
8
2 º 2 º 2
12
2 º 2 º 3
PARTNER
Finding Least Common Multiples
ACTIVITY
Step 3
Multiply the factors that are not crossed out. The least common multiple
of 8 and 12 is 2 º 2 º 2 º 3, or 24.
(Math Journal 2, p. 396; Student Reference Book Glossary)
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1.
Make factor trees and write the prime factorizations for each number.
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a.
15
b.
9
c.
30
2
15
3 5
3
3
Have students locate the term least common multiple in the
2
3
5
Student Reference Book Glossary and read the entry. Ask: What is a
3
5
3
3
2
3
5
15
9
30
common multiple?
A number that is a multiple of two or more given
2.
What is the least common multiple of …
numbers
The quick common denominator is an example of a
45
30
90
a.
9 and 15?
b.
15 and 30?
c.
9 and 30?
common multiple. The smallest number that is a multiple of two
Math Journal 2, p. 396
or more numbers is the least common multiple.
Have students list the first seven multiples of 6 and 9. Ask: What
numbers are in both lists?
The common multiples are 18 and 36.
What is the least common multiple of 6 and 9?
18
Tell students that factor trees also can be used to find the least
common multiple of two numbers. This procedure is similar to
finding the greatest common factor.
Step 1: Refer to the prime factorizations for 18 and 30 from the
previous activity, circling the pairs of common factors.
Step 2: Draw a line through one factor in each of the pairs of
common factors.
∗
∗
Game Master
18 = 2
3
3
∗
∗
30 = 2
3
5
Name
Name
Date
Date
Time
Time
1
2
1
2
∗
∗
∗
Factor Captor 1–110 Grid
Lesson Title
5 = 90
Least common multiple: 2
3
3
4
3
4
3
Step 3: Write the remaining factors in a multiplication expression,
1
1
2
2
3
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9
9
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2 ∗ 3 ∗ 3 ∗ 5 = 90. The least common multiple of 18 and 30 is 90.
11 12 13 14 15 16 17 18 19 20
11 12 13 14 15 16 17 18 19 20
Have partners complete journal page 396. Circulate and assist.
21 22 23 24 25 26 27 28 29 30
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
41 42 43 44 45 46 47 48 49 50
2
Ongoing Learning & Practice
51 52 53 54 55 56 57 58 59 60
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
61 62 63 64 65 66 67 68 69 70
Playing Factor Captor
PARTNER
71 72 73 74 75 76 77 78 79 80
71 72 73 74 75 76 77 78 79 80
ACTIVITY
81 82 83 84 85 86 87 88 89 90
81 82 83 84 85 86 87 88 89 90
(Student Reference Book, p. 306;
91 92 93 94 95 96 97 98 99 100
91 92 93 94 95 96 97 98 99 100
Math Masters, p. 455)
101 102 103 104 105 106 107 108 109 1 10
101 102 103 104 105 106 107 108 109 110
Students practice finding factors of larger numbers and
recognizing prime factors by playing Factor Captor on the
1–110 Grid.
Math Masters, p. 455
Lesson 12 1
917
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