The Ladder Method
For Finding LCD, GCF and
Simplifying Fractions
Becky Afghani, LBUSD Math Curriculum Office, 2003
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
Becky Afghani, LBUSD Math Curriculum Office, 2003
Use the ladder to factor6 and 8
You will divide out any common factors of the two numbers
What number goesinto both 6 and 8?
Now divide both6 and 8 by the 2
Does any # besides 1go into both 3 and 4?No? Then you are done.
Becky Afghani, LBUSD Math Curriculum Office, 2003
Let’s find the Least Common Multiple (LCM) of
6 and 8The LCM is the product of all the
numbers on the left and the bottom.
The LCMof
6 and 8is 24.
Becky Afghani, LBUSD Math Curriculum Office, 2003
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
What about the Greatest Common Factor (GCF) of 6 and
8?The GCF is the product of all the
numbers on the left.
The GCFof
6 and 8is 2.
Becky Afghani, LBUSD Math Curriculum Office, 2003
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
Let’s try some bigger numbers.
Divide out all the common factors down the left side.
What numbergoes into both
24 and 60?Does any #
besides 1go into both 12 and 30?How about6 and 15?
Anything else?No?
You’re done.
Becky Afghani, LBUSD Math Curriculum Office, 2003
x
x
xx
Find the LCM.
=120
The LCMof
24 and 60is 120.
Becky Afghani, LBUSD Math Curriculum Office, 2003
x
x
Find the GCF.
=12
The GCFof
24 and 60is 12.
Becky Afghani, LBUSD Math Curriculum Office, 2003
Practice. Find the LCM and Practice. Find the LCM and
GCF for 28 and 42. GCF for 28 and 42.
LCM = 2 7 2 3 = 84
GCF = 2 7 = 14
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