1. MULTIPLES AND LEAST COMMON MULTIPLES

2. Multiple
The product of a whole number multiplied times any other whole number.
Some multiples of 6
6, 12, 18, 24, 30, 36, 42…

3. Name some multiples of 5
5, 10, 15, 20, 25, 30, 35….

4. Name some multiples of 7
7, 14, 21, 28, 35, 42, 49…. 3

5. Name some multiples of 4
4, 8, 12, 16, 20, 24, 28…

6. Name some multiples of 9
9, 18, 27, 36, 45, 54, 63…..

7. Common Multiple A number that is a multiple of two or more numbers.
6 and 8
6-- 6, 12, 18, 24, 30, 36, 42,48,54,60..
8– 8,16,24, 32,40,48,56,64,72,80…..

8. What is the Least Common Multiple of 6 & 8
6 = 6, 12, 18, 24, 30, 36,42,48,54,60..
8 = 8, 16,24,32,40,48,56,64,72,80…

9. What is the Least Common Multiple of 3 & 9
3 = 3, 6, 9, 12, 15, 21, 24,27,30,33…
9 = 9, 18, 27, 36, 45, 54,63,72,81,90…

10. The Ladder Method (SLED)
For Finding LCD, GCF, distributive property and Simplifying Fractions

11. The Ladder Method (SLED)
is a method of factoring which allows you to factor two numbers at once in order to…
find the LCM of the two numbers
find the GCF of the two numbers
simplify a fraction with these numbers as numerator and denominator
Finding distributive property

12. Use the ladder to factor 6 and 8
You will divide out any common factors of the two numbers 2 6 8 3 4
What number goes
into both 6 and 8?
Now divide both
6 and 8 by the 2
Does any # besides 1
go into both 3 and 4?
No? Then you are done.
ONE YOUR DONE!

13. Let’s find the Least Common Multiple (LCM) of 6 and 8
The LCM is the product of all the numbers on the left and the bottom. x 2 6 8
The LCM of
6 and 8
is 24. 3 4
=24

14. Which numbers in the ladder give you the LCM?
The “L” shape gives you the LCM: multiply the numbers on the left and bottom. # # # # # # # # # # #

15. Let’s try some bigger numbers.
Divide out all the common factors down the left side. 2 24 60
What number
goes into both
24 and 60?
Does any #
besides 1
go into both
12 and 30? 2 12 30
How about
6 and 15?
Anything else? 3 6 15
No?
You’re done.
ONE YOUR DONE 2 5

16. = 120 24 60 2 12 30 6 15 3 5 Find the LCM. The LCM of 24 and 60x
The LCM of
24 and 60
is 120. 24 60 2 12 30 6 15 3 5 =
120

17. G.C.F. is to the left L.C.M. is all of them
Becky Afghani, LBUSD Math Curriculum Office, 2003

18. Practice. Find the LCM and GCF for 28 and 42.7 14 21 2 3
GCF = 2  7 = 14