Least Common
Multiple (LCM)
Least Common Multiple (LCM)
Vocabulary:
 Multiple – a non-zero .
 Least Common Multiple – the least non-zero
common multiple of two or more numbers.
Least Common Multiple (LCM)
When thinking about finding the Least
Common Multiple, or the LCM…
REMEMBER
L…The smallest number
C…all terms in common
M…from their list of multiples
Least Common Multiple (LCM)
Finding the LCM: Method 1 – Prime Factorization
Example 1: Find the LCM of 4 and 9.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors.
4
2
9
2
2·2
3
3
3·3
4: 2 · 2
9:
3·3
2 · 2 · 3 · 3 = 36
LCM = 36
Least Common Multiple (LCM)
Finding the LCM: Method 2 – Find the Product
Example 1: Find the LCM of 4 and 9.
Step 1: For any two numbers, multiply them together
Step 2: Your answer is the LCM of the numbers
4
x9
36
LCM = 36
Least Common Multiple (LCM)
Finding the LCM: Method 1 – Prime Factorization
Example 2: Find the LCM of 10 and 12.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors
10
2
12
5
2·5
3
10: 2 · 5
12: 2
2·3
4
2
2
3·2·2
2 · 5 · 2 · 3 = 60
LCM = 60
Least Common Multiple (LCM)
Finding the LCM: Method 2 – Prime Factorization
Example 3: Find the LCM of 12 and 16.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors
12
3
16
4
2
4
4
2
3·2·2
2
12: 2 · 2 ·
3
16: 2 · 2 · 2 · 2
2 2
2·2·2·2
2
2 · 2 · 2 · 2 · 3 = 48
LCM = 48
Least Common Multiple (LCM)
Guided Practice Problems
Directions: Find the LCM for each number set.
1. 9 and 12
2. 4, 8, and 12
3. 2, 3, 6, and 8
Least Common Multiple (LCM)
Guided Practice Problems
Directions: Find the LCM for each number set.
1. 9 and 12
=> 6
2. 4, 8, and 12
=> 16
3. 2, 3, 6, and 8
=> 24
Least Common Multiple (LCM)
Independent Practice Problems
Directions: Find the LCM for each number set.
1. 6 and 10
2. 2, 4, and 5
3. 4, 6, and 8
Least Common Multiple (LCM)
Independent Practice Problems
Directions: Find the LCM for each number set.
1. 6 and 10
=> 30
2. 2, 4, and 5
=> 20
3. 4, 6, and 8
=> 24