Warm Up

1
Warm Up
Problem of the Day
Lesson Presentation
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 persons 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
(No Transcript)
7
Additional Example 1 Consumer Application 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 no muffins 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.
8
Check It Out Example 1
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.
9
The smallest number that is a multiple of two or
more numbers is the least common multiple (LCM).
In Additional Example 1, the LCM of 8 and 12 is
24.
10
Additional Example 2A Using Multiples to Find
the LCM Find the least common multiple
(LCM). Method 1 Use a number line. 3 and 4
Use a number line to skip count by 3 and 4.
The least common multiple (LCM) of 3 and 4 is 12.
11
Additional Example 2B Using Multiples to Find
the LCM Find the least common multiple
(LCM). Method 2 Use a list.
4, 5, and 8
4 4, 8, 12 , 16, 20, 24, 28, 32, 36, 40,
44, . . .
List multiples of 4, 5, and 8.
5 5, 10, 15, 20, 25, 30, 35, 40, 45, . . .
Find the smallest number that is in all the
lists.
8 8, 16, 24, 32, 40, 48, . . .
LCM 40
12
(No Transcript)
13
Additional Example 2C Using Multiples to Find
the LCM Find the least common multiple
(LCM). Method 3 Use prime factorization. 6 and 20
6 2 3
Write the prime factorization of each number.

20 2 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
14
Additional Example 2D Using Multiples to Find
the LCM 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 22
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
15
Check It Out Example 2A Find the least common
multiple (LCM). Method 1 Use a number line. 2
and 3
Use a number line to skip count by 2 and 3.
The least common multiple (LCM) of 2 and 3 is 6.
16
Check It Out Example 2B Find the least common
multiple (LCM). Method 2 Use a list. 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.
17
Check It Out Example 2C Find the least common
multiple (LCM). Method 3 Use prime
factorization. 4 and 10
4 2 2
Write the prime factorization of each number.

10 2 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
18
Check It Out Example 2D 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
19
Lesson Quiz
Find the least common multiple (LCM). 1. 6, 14
2. 9, 12 3. 5, 6, 10 4. 12, 16, 24, 36 5.
Two students in Mrs. Albrings preschool class
are stacking blocks, one on top of the other.
Reeces blocks are 4 cm high and Maddys 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