1. Least Common Multiple

2. Multiples
A multiple is formed by multiplying a given number by the counting numbers.
The counting numbers are 1, 2, 3, 4, 5, 6, etc.

3. Example: List the multiples of 4:
So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc.
Counting Numbers

4. What are the first five multiples of 13?
13 x 1 =13
13 x 2 = 26
13 x 3 = 39
13 x 4 = 52
13 x 5 = 65
13, 26, 39, 52, 65

5. Find the Missing Multiples
6, 12, 18, ____, ____
___, 6, 9, 12, ____, ____, 21
___, 24, 36, 48, 60, ____ 24 30 3 15 18 12 72

6. Least Common Multiple (LCM)
The least common multiple is the smallest number that is common between two lists of multiples.

7. EXAMPLE: Find the LCM of 12 and 18
The multiples of 12:
12 x 1 = 12
12 x 2 =24
12 x 3 = 36
12 x 4 = 48
12 x 5 =60
The multiples of 18:
18 x 1 = 18
18 x 2 = 36
18 x 3 = 54
18 x 4 = 72
18 x 5 = 90

8. 12, 24, 36, 48, 60
18, 36, 54, 72, 90
The first number you see in both lists is 36.
The least common multiple of 12 and 18 is 36.

9. Example 2: Find the LCM of 9 and 10
9, 18, 27, 36, 45, 54, 63, 72
81, 90, 99
10, 20, 30, 40, 50, 60, 70, 80
90, 100, 110
If you don’t see a common multiple, make each list go further.
The LCM of 9 and 10 is 90

10. Example 3: Find the LCM of 4 and 12
4, 8, 12, 16
12, 24, 36
Answer: 12

11. Using Prime Factorization to find the LCM
Make factor trees for each number. Write the prime factorization in exponent form.
Identify all of the prime numbers among the prime factorizations. Every prime number will be used.
When the same prime number occurs in more than one prime factorization, select the prime that there’s more of (for example, 25 beats 22.)
Multiply your prime numbers to get the LCM.

12. Example: Find the LCM of 88 and 102
102 = 2 x 3 x 17
2 x 51
2 x 44
LCM: 23 x 3 x 11 x 17 = 4,488
2 x 22
3 x 17
We have to use every prime number. The numbers we will use are 2, 3, 11, and 17.
2 x 11
We have 2 in both places. Select the “bigger” one. 23 beats regular 2.

13. Homework Time