MSM07G7_RESBK_Ch02_060-067.pe
12/29/05
9:32 PM
Page 65
Name
LESSON
Date
Class
Problem Solving
2-8 Least Common Multiple
Write the correct answer.
1. Earth revolves around the sun every
year. Jupiter revolves around the sun
every 12 years. If Earth and Jupiter
passed the same point of the sun
sometime in 2002, when will they
pass that point together again?
2. House representatives are elected
every 2 years. The President of the
United States is elected every
4 years. Both will be elected in 2008.
When is the next year after 2008
both will be elected?
2014
2012
3. A cat runs a mile every 2 minutes. A
squirrel runs a mile every 5 minutes.
A cat and a squirrel start together
running around a 1-mile track. How
long will it be before they meet at the
starting point?
4. A car manual recommends changing
the oil every 5,000 miles and
inspecting the engine coolant system
every 15,000 miles. At how many
miles will both be done together for
the first time? for the second time?
10 minutes
15,000 mi; 30,000 mi
Choose the letter for the best answer.
5. Mr. Walters receives a dividend every
5 months and a royalty payment
every 6 months. He received both in
January 2006. When is the next time
he would receive both payments in
the same month?
A January 2007
B April 2008
C July 2006
D July 2008
嘷
6. Rag Rite Cloth Store always rounds
amounts less than whole yards up to
the next yard for ribbon purchases.
The ribbon that you want to buy comes
in rolls of 8 feet. How many rolls
should you buy to get the best buy?
F 1 roll
G 2 rolls
H 3 rolls
嘷
J 4 rolls
7. The sanitation department picks up
recyclable plastics every 3 days. The
paper recycling center picks up
papers every 4 days. They both
picked up on May 4. When will they
next pick up on the same day?
A May 7
B May 12
C May 11
D May 16
嘷
8. Hal and Jess both volunteer at the
local nursing home. Hal volunteers
every 6 days, and Jess volunteers
every 8 days. They were both there
on Monday. In how many days will
they both volunteer together again?
F in 14 days
G in 24 days
嘷
H in 48 days
J in 2 days
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
65
Holt Mathematics
Challenge
2-8 Multiple Solutions
Reteach
2-8 Least Common Multiple
LESSON
LESSON
Write the two numbers from each box that have the lowest least
common multiple. Then write the LCM.
The least common multiple (LCM) of two numbers is the least
multiple that the two numbers have in common.
• To list the multiples of a number, multiply the number by 1, 2, 3,
and so on.
8•1
8•2
8•3
8•4
8•5
Multiples of 8
8
16
24
32
40
6•1
6•2
6•3
6•4
6•5
6
12
18
24
30
1.
3.
Multiples of 6
• To find the least common multiple of 6 and 8, list several multiples
of each number.
Step 1: List multiples of the greater number.
5.
Multiples of 8: 8 16 24 32 40
7.
Step 2: List the multiples of the lesser number
until you find a multiple that is common
to each list.
Multiples of 6: 6 12 18 24
Since 24 is the first number common to both lists, it is the least
common multiple. So the LCM of 6 and 8 is 24.
9.
5 12
Numbers:
6 8
LCM:
2 10
Numbers:
LCM:
6 4
Numbers:
2; 3
4.
4; 6
6.
12
7 5
LCM:
8 10
Numbers:
6 5
LCM:
15 10
Numbers:
LCM:
2.
6
5 3
7 8
6; 12
12
5; 10
8.
10
10; 15
2 7
Numbers:
9 10
LCM:
7 2
Numbers:
2; 10
10
10 12
LCM:
9 10
Numbers:
15 45
LCM:
24 35
Numbers:
32 14
LCM:
10. 3 10
30
2; 10
10
10; 15
30
14; 35
70
3; 12
Numbers:
12 7
12
LCM:
Find the least common multiple (LCM).
Use the table at the bottom of the page to solve the riddle. In
the middle row, write the LCM of each exercise above the
exercise number. Then choose the letter from the Answer Key
that matches the LCM and write it in the appropriate box.
1. 4, 9
Multiples of 9: 9, 18, 27, 36, 45, 54
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36
36
LCM of 4 and 9:
Answer Key
2. 6, 7
Multiples of 7: 7, 14,
21
,
28
,
35
,
42
,
49
Multiples of 6: 6, 12,
18
,
24
,
30
,
36
,
42
56
3. 15, 20
Multiples of 20:
20
,
40
,
60
,
80
Multiples of 15:
15
,
30
,
45
,
60
LCM of 15 and 20:
T
E
H
70
6
30
12
10
,
100
T
30
H
10
E
12
C
70
H
10
E
12
E
12
T
30
A
6
H
10
9
4
5
8
2
1
10
6
3
7
60
36
5. 16, 20
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
80
6. 4, 6, 9
63
36
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
64
Holt Mathematics
Reading Strategies
2-8 Focus on Vocabulary
Problem Solving
2-8 Least Common Multiple
LESSON
LESSON
Write the correct answer.
1. Earth revolves around the sun every
year. Jupiter revolves around the sun
every 12 years. If Earth and Jupiter
passed the same point of the sun
sometime in 2002, when will they
pass that point together again?
2. House representatives are elected
every 2 years. The President of the
United States is elected every
4 years. Both will be elected in 2008.
When is the next year after 2008
both will be elected?
2014
2012
3. A cat runs a mile every 2 minutes. A
squirrel runs a mile every 5 minutes.
A cat and a squirrel start together
running around a 1-mile track. How
long will it be before they meet at the
starting point?
4. A car manual recommends changing
the oil every 5,000 miles and
inspecting the engine coolant system
every 15,000 miles. At how many
miles will both be done together for
the first time? for the second time?
10 minutes
15,000 mi; 30,000 mi
Choose the letter for the best answer.
A multiple of a number is the product of that number and another
factor.
Multiples of 5 are the numbers you get when you multiply by 5.
1•5ⴝ5
2 • 5 ⴝ 10
3 • 5 ⴝ 15
4 • 5 ⴝ 20
The multiples of 5 listed above are 5, 10, 15, 20.
You can continue to count by 5’s to list more multiples of 5: 25, 30,
35, and so on.
Common means something that is shared. A common multiple of two
numbers is a multiple that the two numbers share, or have in common.
Multiples of 5
Multiples of 4
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60
In the example above, you can see the multiples that are common
to both 4 and 5. They are 20, 40, and 60.
The least common multiple (LCM) of two numbers is the smallest
of the common multiples. 20 is the smallest, or least common,
multiple of 4 and 5.
Answer each question.
5. Mr. Walters receives a dividend every
5 months and a royalty payment
every 6 months. He received both in
January 2006. When is the next time
he would receive both payments in
the same month?
A January 2007
B April 2008
C July 2006
D July 2008
嘷
6. Rag Rite Cloth Store always rounds
amounts less than whole yards up to
the next yard for ribbon purchases.
The ribbon that you want to buy comes
in rolls of 8 feet. How many rolls
should you buy to get the best buy?
F 1 roll
G 2 rolls
H 3 rolls
嘷
J 4 rolls
7. The sanitation department picks up
recyclable plastics every 3 days. The
paper recycling center picks up
papers every 4 days. They both
picked up on May 4. When will they
next pick up on the same day?
A May 7
B May 12
C May 11
D May 16
嘷
8. Hal and Jess both volunteer at the
local nursing home. Hal volunteers
every 6 days, and Jess volunteers
every 8 days. They were both there
on Monday. In how many days will
they both volunteer together again?
F in 14 days
G in 24 days
嘷
H in 48 days
J in 2 days
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
A
11. What animal copies from the others on a math test?
42
LCM of 6 and 7:
4. 12, 18
,
C
65
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
1. What is a multiple?
Possible answer: the answers or products when you multiply
by a certain number
2. What does the word common mean?
something that is shared
3. What is a common multiple?
multiples that two numbers share, or have in common
4. What is the least common multiple?
the smallest multiple that two numbers have in common
5. Write the first 9 multiples of 2.
2, 4, 6, 8, 10, 12, 14, 16, 18
6. Write the first 9 multiples of 3.
3, 6, 9, 12, 15, 18, 21, 24, 27
7. Write the common multiples for both 2 and 3.
8. What is the least common multiple for 2 and 3?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
108
66
6, 12, and 18
6
Holt Mathematics
Holt Mathematics