1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Write the first five multiples of each number.
1. 5
2. 6
3. 10
4. 12
5, 10, 15, 20, 25
6, 12, 18, 24, 30
10, 20, 30, 40, 50
12, 24, 36, 48, 60

3. Problem of the Day
Greg, Sam and Mary all work at the same high school. One of them is a principal, one of them is a teacher, and one of them is a janitor. Sam is older than Mary. Mary does not live in the same town as the principal. The teacher, the oldest of the three, often plays golf with Greg. What is each person’s job?
Greg, principal; Sam, teacher; Mary, janitor

4. Learn to find the least common multiple (LCM) of a group of numbers.

5. Vocabulary
least common multiple (LCM)‏

6. The smallest number that is a multiple of two or more numbers is the least common multiple (LCM).

7. Find the least common multiple (LCM). 6 and 20
6 = 2 • 3
Write the prime factorization of each number.
20 = • 2 • 5
Line up the common factors.
2 • 3 • 2 • 5
To find the LCM, multiply one number from each column.
2 • 3 • 2 • 5 = 60
LCM: 60

8. Find the least common multiple (LCM). Use a list.
4, 5, and 8
4: 4, 8, 12 , 16, 20, 24, 28, 32, , 40, 44, . . .
List multiples of 4, 5, and 8.
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, . . .
8: 8, 16, 24, 32, 40, 48, . . .
Find the smallest number that is in all the lists.
LCM: 40

9. Find the least common multiple (LCM). 15, 6, and 4
15 = 3 • 5
Write the prime factorization of each number in exponential form.
6 = 3 • 2
4 =
To find the LCM, multiply each prime factor once with the greatest exponent used in any of the prime factorizations.
3 • 5 • 22
3 • 5 • 22 = 60
LCM: 60

10. English muffins come in packs of 8, and eggs come in cartons of 12
English muffins come in packs of 8, and eggs come in cartons of 12. If there are 24 students, what is the least number of packs and cartons needed so that each student has a muffin sandwich with one egg and there are none left over?
Draw muffins in groups of 8. Draw eggs in groups of 12. Stop when you have drawn the same number of each.
There are 24 English muffins and 24 eggs.
So 3 packs of English muffins and 2 cartons of eggs are needed.

11. Dog cookies come in packages of 6, and bones in bags of 9
Dog cookies come in packages of 6, and bones in bags of 9. If there are 18 dogs, what is the least number of packages and bags needed so that each dog has a treat box with one bone and one cookie and there are no bones or cookies left over?
Draw cookies in groups of 6. Draw bones in groups of 9. Stop when you have drawn the same number of each.
There are 18 dog cookies and 18 bones.
So 3 packages of dog cookies and 2 bags of bones are needed.

12. Hot dogs come in packs of 8. Hot dog rolls come in packs of 12.
What is the least number of packs of each you need to have
enough to serve 24 people and have none left over?

13. Invitations come in packs of 12 and stamps come in sheets of 10.
What is the least number of each you need to invite 60 people and
have no stamps or invitations left over?

14. Find the least common multiple (LCM). 3, 4, and 9
3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, . . .
List multiples of 3, 4, and 9.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, …
Find the smallest number that is in all the lists.
9: 9, 18, 27, 36, 45, . . .
The least common multiple of 3, 4, and 9 is 36.

15. Find the least common multiple (LCM). 4 and 10
4 = 2 • 2
Write the prime factorization of each number.
10 = • 5
Line up the common factors.
2 • 2 • 5
To find the LCM, multiply one number from each column.
2 • 2 • 5 = 20
LCM: 20

16. Find the least common multiple (LCM).
12, 6, and 8
12 = 22 • 3
Write the prime factorization of each number in exponential form.
6 = 2 • 3
8 = 23
To find the LCM, multiply each prime factor once with the greatest exponent used in any of the prime factorizations.
23 • 3
23 • 3 = 24
LCM: 24

17. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

18. Lesson Quiz
Find the least common multiple (LCM).
1. 6, , 12
3. 5, 6, , 16, 24, 36
5. Two students in Mrs. Albring’s preschool class are stacking blocks, one on top of the other. Reece’s blocks are 4 cm high, and Maddy’s blocks are 9 cm high. How tall will their stacks be when they are the same height for the first time? 42 36 30
144
36 cm

19. Lesson Quiz for Student Response Systems
1. Identify the least common multiple (LCM).
8, 18
A C. 72
B D. 64

20. Lesson Quiz for Student Response Systems
2. Identify the least common multiple (LCM).
9, 24
A C. 52
B D. 27

21. Lesson Quiz for Student Response Systems
3. Identify the least common multiple (LCM).
3, 15, 18
A C. 54
B D. 24

22. Lesson Quiz for Student Response Systems
4. Identify the least common multiple (LCM).
9, 12, 18, 27
A C. 172
B D. 216

23. Lesson Quiz for Student Response Systems
5. Water colors come in boxes of 6 and brushes come in packets of 10. Tom wants to give each of 30 students a water color and a brush. What is the least number of boxes and packs he should buy so there are none left over?
A. 3 boxes of water colors and 5 packs of brushes
B. 5 boxes of water colors and 3 packs of brushes
C. 4 boxes of water colors and 2 packs of brushes
D. 2 boxes of water colors and 4 packs of brushes