# Find the least common multiple (LCM).

```Wednesday, October 13 (Blue)
Thursday, October 14 (Gold)
1. Fill in planner (Practice 5-1)
2. Bell Work (Write the prime factorization of
each number)
Objective
• SWBAT find the Least Common Multiple (LCM)
and compare and order fractions.
Vocabulary
Multiple
least common multiple (LCM)
least common denominator (LCD)
multiple
A multiple of a number is the
product of the number and any
nonzero whole number.
least common multiple (LCM): The
smallest number that is a multiple of two
or more numbers.
least common denominator (LCD): The
smallest number that is the multiple of two
or more denominators.
Today, the school’s baseball and soccer teams
had games. The baseball team plays every 7
days. The soccer team plays every 3 days. When
will the teams have games on the same day
again?
3,7
7: 7, 14, 21 , 28, 35, 42, . . .
3: 3, 6, 9, 12, 15, 18, 21, . . .
List multiples of 3 and 7.
Find the smallest number
that is in all the lists.
LCM: 21. In 21 days, both teams will have game on
the same day again.
Remember!
The prime factorization of a number is
the number written as a product of its
prime factors.
Example 2: Find the LCM of 16 and 36
16 = 24
36 = 22• 32
24 • 32
16 • 9 = 144
LCM: 144
Write the prime factorizations
Use the greatest power of
each factor.
Multiply.
Example 3: Find the LCM of 5a4 and 15a
5a4 =
5 • a4
15a = 3• 5 •a
3 • 5• a4
15a4
LCM: 15a4
Write the prime factorizations
Use the greatest power of
each factor.
Multiply.
negative
<
positive
7
-7
7
7
7
21
21
21
84
28
56
28
84
<
7
84
84
<
<
<
20
60
48
45
180
60
4
2
12
56m
75xy
<
>
1 5 2
, ,
6 12 3
<
1 3 1 7
, , ,
5 10 2 12
Additional Example 2D: Using Multiples to Find
the LCM
Find the least common multiple (LCM).
15, 6, and 4
15 = 3 • 5
6=3•
2
4=
22
Write the prime factorization of
each number in exponential form.
To find the LCM, multiply each
prime factor once with the
3 • 5 • 22
greatest exponent used in any of
3 • 5 • 22 = 60 the prime factorizations.
LCM: 60
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.
0
1
2
3
4
5
6
The least common multiple (LCM) of 2 and 3 is 6.
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.
Check It Out: Example 2C
Find the least common multiple (LCM).
Method 3: Use prime factorization.
4 and 10
4=2•2
10 = 2
•5
Write the prime factorization of
each number.
Line up the common factors.
2•2 •5
2 • 2 • 5 = 20
LCM: 20
To find the LCM, multiply one
number from each column.
Check It Out: Example 2D
Find the least common multiple (LCM).
12, 6, and 8
12 = 22 • 3
6=2• 3
Write the prime factorization of
each number in exponential form.
8 = 23
23 • 3
23 • 3 = 24
LCM: 24
To find the LCM, multiply each
prime factor once with the
greatest exponent used in any of
the prime factorizations.
Lesson Quiz
Find the least common multiple (LCM).
1. 6, 14 42
3. 5, 6, 10 30
2. 9, 12
36
4. 12, 16, 24, 36
144
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?
36 cm
```