1. For Finding LCD, GCF and Simplifying Fractions
The Ladder Method
For Finding LCD, GCF and Simplifying Fractions
Becky Afghani, LBUSD Math Curriculum Office, 2003

2. Becky Afghani, LBUSD Math Curriculum Office, 2003
The Ladder Method...
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
Becky Afghani, LBUSD Math Curriculum Office, 2003

3. 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.
Becky Afghani, LBUSD Math Curriculum Office, 2003

4. 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
Becky Afghani, LBUSD Math Curriculum Office, 2003

5. Which numbers in the ladder give you the LCM?
The “L” shape gives you the LCM: multiply the numbers on the left and bottom. # # # # # # # # # # #
Becky Afghani, LBUSD Math Curriculum Office, 2003

6. What about the Greatest Common Factor (GCF) of 6 and 8?
The GCF is the product of all the numbers on the left. 2 6 8
The GCF of
6 and 8
is 2. 3 4
Becky Afghani, LBUSD Math Curriculum Office, 2003

7. Which numbers in the ladder give you the GCF?
Multiply the numbers on the left only for the GCF. # # # # # # # # # # #
Becky Afghani, LBUSD Math Curriculum Office, 2003

8. How can we use the Ladder Method to simplify ?
The simplified numerator and denominator are on the bottom.
simplifies to 2 6 8 3 4
Becky Afghani, LBUSD Math Curriculum Office, 2003

9. Which numbers in the ladder give you the simplified fraction?
The numbers on the bottom of the ladder are your simplified numerator and denominator. # # # # # # # # # # #
Becky Afghani, LBUSD Math Curriculum Office, 2003

10. 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. 2 5
Becky Afghani, LBUSD Math Curriculum Office, 2003

11. Becky Afghani, LBUSD Math Curriculum Office, 2003
Find the LCM. x
The LCM of
24 and 60
is 120. 24 60 2 12 30 6 15 3 5 =
120
Becky Afghani, LBUSD Math Curriculum Office, 2003

12. Becky Afghani, LBUSD Math Curriculum Office, 2003
Find the GCF. x
The GCF of
24 and 60
is 12. 24 60 2 12 30 6 15 3 5 = 12
Becky Afghani, LBUSD Math Curriculum Office, 2003

13. Becky Afghani, LBUSD Math Curriculum Office, 2003
Simplify
simplifies to . 24 60 2 12 30 6 15 3 5
Becky Afghani, LBUSD Math Curriculum Office, 2003

14. Practice. Find the LCM and GCF for 28 and 42. Simplify .7 14 21
Simplified fraction = 2 3
Becky Afghani, LBUSD Math Curriculum Office, 2003

15. Becky Afghani, LBUSD Math Curriculum Office, 2003
Extension Questions
1. Do you have to factor out prime numbers?
2. Can you factor three numbers at once and still get the right GCF and LCM? Try factoring small numbers to find out - like 4, 6, and 8. 28 42 2 14 21 7 3
Becky Afghani, LBUSD Math Curriculum Office, 2003