&&66
)LQGDOOIDFWRUSDLUVIRUDZKROHQXPEHULQWKHUDQJH±
NS 1.4*2$
Determine
the prime factors of all numbers through 50 and write
5HFRJQL]HWKDWDZKROHQXPEHULVDPXOWLSOHRIHDFKRILWVIDFWRUV'HWHUPLQHZKHWKHUD
numbers as the product of their prime factors using exponents
JLYHQZKROHQXPEHULQWKHUDQJH±LVDPXOWLSOHRIDJLYHQRQHGLJLWQXPEHU
to show multiples of a factor (e.g., 24 ! 2 " 2 " 2 " 3 ! 8 x 3).
'HWHUPLQHZKHWKHUDJLYHQZKROHQXPEHULQWKHUDQJH±LVSULPHRUFRPSRVLWH
UNDERLYING SKILLS AND CONCEPTS:
find the multiples of a number;
use multiplication facts;
skip counting
Find the Least Common Multiple
Multiples of a number are that number multiplied by another one.
Any number has an infinite number of multiples: you can multiply it
by 2, 3, ...
If you have two numbers, each has its own set of multiples.
Some of these multiples may be common to both numbers.
The smallest of the common ones is called the least common multiple.
The least common multiple is sometimes abbreviated as LCM.
1
96
84
72
Find the least common multiple of 12 and 16.
!
!
Multiples of 12: 12, 24, 36, 48, 60, 72, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, ...
The least number in both lists is 48.
48 is the least common multiple of 12 and16.
E x am p l E
80
60
Make a list of multiples for each number.
Use skip counting, or keep adding 12 or 16.
64
48
36
!
24
Hey,
They are
writing
12
my
multiples.
Mr.
Multiple
48
32
Th
es
ea
re
mi
ne
.
M s.
16
Mu lti ple
2
Find the LCM of 5 and 6.
First remember, LCM stands for least common multiple.
Make a list of multiples for each number. Use skip counting.
!
Multiples of 5: 5, 10, 15, 20, 25, 30, ..
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
The first multiple in both lists is 30.
!
Hey, this LCM happens
to be the product of the
numbers. 5 x 6 = 30
LCM
So, 30 is the LCM of 5 and 6.
page 172
Chapter 15 – Lesson 2
E – © CSL Associates, Inc. All rights reserved.
E x am p l E
Name
P RAC T I C E
Use any method to find the least common multiple for each pair of numbers.
1. 2, 8
8
5. 8, 10
40
9. 1, 91
91
13. 9, 12
36
2. 6, 12
12
6. 8, 18
72
10. 20, 15
60
14. 10, 14
70
3. 6, 14
42
7. 12, 12
12
11. 25, 10
50
15. 11, 8
88
4. 4, 8
8
8. 12, 30
60
12. 16, 32
32
16. 14, 21
42
Use any method to find the least common multiple for each set of numbers.
17. 4, 8, 2
8
19. 12, 30, 10 60
21. 16, 32, 8
32
23. 14, 21, 7
42
18. 4, 8, 12
24
20. 12, 30, 60 60
22. 16, 32, 3
96
24. 14, 21, 28 84
Solve. Explain how you decided.
25. Hot dogs come 10 to a package. Rolls come 8 to a package.
E – © CSL Associates, Inc. All rights reserved.
What is the least number of each that you need to
buy to have exactly one hot dog for each roll?
You need 40 of each.
26. How many packages of hot dogs do you need?
4
27. How many packages of rolls do you need?
5
Circle the correct choice.
28. Which is the LCM of
both 14 and 21?
A
C
7
42
Math
Reasoning
B 35
D 294
29. 42 is the least common
30. Which of these pairs of
multiple of what pair of
numbers?
numbers does not have
a least common
multiple?
F
H
42, 84
40, 2
G 9, 42
J 6, 14
A
C
0, 1
2, 2
B 1, 1
D 1, 10
Products and Multiples
MR 1.1, 2.4
31. Sandor says, “The Least Common Multiple of two numbers is always the product of the
numbers.” Do you agree or disagree?
Explain your answer and give two different examples.
The product of 2 numbers is always a common multiple.
But it is not necessarily the LCM. When both numbers have a
common factor, the product divided by the common factor will
give the LCM.
Chapter 15 – Lesson 2
page 173
MCX94.HW.CL.G5.FM&Lesson.v211
8/2/04
18:03
Page 116
Name
…at home!
P RAC T I C E
Use any method to find the least common multiple for each pair of numbers.
1. 2, 12
12
5. 8, 20
40
9. 1, 37
37
13. 7, 9
63
2. 8, 12
24
6. 8, 24
24
10. 25, 10
50
14. 12, 15
60
3. 6, 18
18
7. 12, 16
48
11. 20, 15
60
15. 11, 6
66
4. 4, 12
12
8. 14, 28
28
12. 8, 10
40
16. 7, 21
21
Use any method to find the least common multiple for each set of numbers.
9
19. 6, 24, 10
120
36
20. 6, 24, 48
48
17. 6, 9, 3
18. 6, 12, 18
21. 15, 30, 5
30
24
23. 24, 12, 4
22. 15, 30, 10 30
24. 24, 12, 48 48
Solve. Explain how you decided.
25. Peanut butter cracker packs come 24 to a box. Juice boxes come
10 to a pack. What is the least number of each that you need to buy
to have exactly one cracker pack for each juice box? You need 120 of each.
5
26. How many boxes of cracker packs do you need?
12
27. How many packs of juice boxes do you need?
28. Which is the LCM of
both 12 and 15?
A
C
3
60
Math
Reasoning
B 27
D 180
29. 28 is the least common
30. Which of these pairs of
multiple of what pair of
numbers?
F
H
28, 56
20, 8
G 7, 28
J 6, 14
Products and Multiples
numbers does not have a
least common multiple?
A
C
0, 1
4, 4
B 10, 10
D 1, 100
MR 1.1, 2.4
31. When is the Least Common Multiple of two numbers the product of the numbers?
Explain your answer and give two different examples.
When numbers do not have any common factors.
LCM for 5 and 6:
factors of 5: 10, 15, 25, 30
factors of 6: 12, 18, 24, 30
LCM for 3 and 4:
factors of 3:, 6, 9, 12
factors of 4, 8, 12
page 116
Home Resource and Homework
Chapter 15 Lesson 2
E – © CSL Associates, Inc. All rights reserved.
Circle the correct choice.
MCX94TEG5CH01_32.v7.4.2 2/24/01 19:46 Page 319
Name
P RAC T I C E
Use any method to find the least common multiple for each pair of numbers.
1. 2, 8
8
5. 8, 10
40
9. 1, 91
91
13. 9, 12
36
2. 6, 12
12
6. 8, 18
72
10. 20, 15
60
14. 10, 14
70
3. 6, 14
42
7. 12, 12
12
11. 25, 10
50
15. 11, 8
88
4. 4, 8
8
8. 12, 30
60
12. 16, 32
32
16. 14, 21
42
Use any method to find the least common multiple for each set of numbers.
17. 4, 8, 2
8
19. 12, 30, 10 60
21. 16, 32, 8
32
23. 14, 21, 7
42
18. 4, 8, 12
24
20. 12, 30, 60 60
22. 16, 32, 3
96
24. 14, 21, 28 84
Solve. Explain how you decided.
25. Hot dogs come 10 to a package. Rolls come 8 to a package.
E – © CSL Associates, Inc. All rights reserved.
What is the least number of each that you need to
buy to have exactly one hot dog for each roll?
You need 40 of each.
26. How many packages of hot dogs do you need?
4
27. How many packages of rolls do you need?
5
Circle the correct choice.
28. Which is the LCM of
both 14 and 21?
A
C
7
42
Math
Reasoning
B 35
D 294
29. 42 is the least common
30. Which of these pairs of
multiple of what pair of
numbers?
numbers does not have
a least common
multiple?
F
H
42, 84
40, 2
G 9, 42
J 6, 14
A
C
0, 1
2, 2
B 1, 1
D 1, 10
Products and Multiples
MR 1.1, 2.4
31. Sandor says, “The Least Common Multiple of two numbers is always the product of the
numbers.” Do you agree or disagree?
Explain your answer and give two different examples.
The product of 2 numbers is always a common multiple.
But it is not necessarily the LCM. When both numbers have a
common factor, the product divided by the common factor will
give the LCM.
Chapter 15 – Lesson 2
Student Book Page
page 173
Name
…at home!
P RAC T I C E
Use any method to find the least common multiple for each pair of numbers.
1. 2, 12
12
5. 8, 20
40
9. 1, 37
37
13. 7, 9
63
2. 8, 12
24
6. 8, 24
24
10. 25, 10
50
14. 12, 15
60
3. 6, 18
18
7. 12, 16
48
11. 20, 15
60
15. 11, 6
66
4. 4, 12
12
8. 14, 28
28
12. 8, 10
40
16. 7, 21
21
Use any method to find the least common multiple for each set of numbers.
9
19. 6, 24, 10
120
36
20. 6, 24, 48
48
17. 6, 9, 3
18. 6, 12, 18
21. 15, 30, 5
30
24
23. 24, 12, 4
22. 15, 30, 10 30
24. 24, 12, 48 48
Solve. Explain how you decided.
25. Peanut butter cracker packs come 24 to a box. Juice boxes come
10 to a pack. What is the least number of each that you need to buy
to have exactly one cracker pack for each juice box? You need 120 of each.
5
26. How many boxes of cracker packs do you need?
12
27. How many packs of juice boxes do you need?
28. Which is the LCM of
both 12 and 15?
A
C
3
60
Math
Reasoning
B 27
D 180
29. 28 is the least common
30. Which of these pairs of
multiple of what pair of
numbers?
F
H
28, 56
20, 8
G 7, 28
J 6, 14
Products and Multiples
numbers does not have a
least common multiple?
A
C
0, 1
4, 4
B 10, 10
D 1, 100
MR 1.1, 2.4
31. When is the Least Common Multiple of two numbers the product of the numbers?
Explain your answer and give two different examples.
When numbers do not have any common factors.
LCM for 5 and 6:
factors of 5: 10, 15, 25, 30
factors of 6: 12, 18, 24, 30
LCM for 3 and 4:
factors of 3:, 6, 9, 12
factors of 4, 8, 12
page 116
Home Resource and Homework
Chapter 15 Lesson 2
E – © CSL Associates, Inc. All rights reserved.
Circle the correct choice.