1. For Finding LCD, GCF and Simplifying Fractions
The Ladder Method
For Finding LCD, GCF and Simplifying Fractions

2. 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

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.

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

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. # # # # # # # # # # #

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

7. Which numbers in the ladder give you the GCF?
Multiply the numbers on the left only for the GCF. # # # # # # # # # # #

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

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. # # # # # # # # # # #

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

11. = 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

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

13. Simplify
simplifies to . 24 60 2 12 30 6 15 3 5

14. Practice. Find the LCM and GCF for 28 and 42. Simplify .7 14 21
Simplified fraction = 2 3

15. 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