1. Least Common Multiple

2. What is a multiple?
A multiple of a whole number is the product of the whole number and any number
Example the multiples of 8 are
8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32

3. What are the multiples of 5?

4. What are the multiples of 8?

5. What is a LCM?
LCM is the smallest number other than 0 that is a multiple of 2 or more whole numbers

6. Find the LCM by making a list
List all the nonzero multiples
9: 9, 18, 27, 36, 45, 54, 63, 72
12: 12, 24, 36, 48, 60, 72
Identify the LCM from the list
The LCM of 9 and 12 is 36.

7. HINTS
The LCM cannot be larger than the product of the two whole numbers.
The LCM of 3 and 4 cannot be larger than 12 because 3 x 4 = 12
Use your multiplication chart to help find the multiples

8. A quick review What is prime factorization?
A composite number expressed as a product of primes
Factor Trees 15

9. Find the LCM by using prime factorization
Find the LCM of 15 and 25

10. 15 and 25 cont. Identify common factors
15: 3, 5
25: 5, 5
Find the product of the common and remaining factors
3 x 5 x 5 = 75

11. School Dance Team
The school dance team lines up in even rows of 3, 4, or 5 at practice. What is the least number of people needed to line up in rows or 3, 4, or 5?

12. To find the number of members needed you find the LCM for 3, 4 or 5

13. Use the list method

14. Using prime factorization

15. Fruit word problem
Jessica is filling bags of fruit. She fills one bag with just apples, a second bag with just oranges, and a third bag with just pears. If each apple weighs 6 ounces, each orange weighs 8 ounces, and each pear weighs 9 ounces, at what point will each of the bags have the same weight?

16. List Method

17. Prime Factorization

18. The bags will have the same weight at 2  2  2  3  3 or 72 ounces.

19. On a calculator TI 34 II 2nd key ) (math) Arrow over to lcm Enter key
Enter 1st number
Division key (,)
Enter 2nd number )
TI 34 II Multiview
Math key
Enter
Enter 1st number
2nd key
. (,)
Enter 2nd number )