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Finding Least Common Denominators
Objectives:
1. The teacher will explore using Cuisenaire Rods to determine the Least common
Denominator of two unlike fractions .
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TOPIC: FINDING THE LEAST COMMON DENOMINATOR [FINDING
LCMs]
Materials: CUISENAIRE RODS
1. As a group , use Cuisenaire Rods and work through these steps to find the LCM (6, 8).
Our Goal:
We wish to find the LCM (6, 8). We need to find a Cuisenaire Rod train that is:
i. A multiple of 6
ii . A multiple of 8
Iii. The smallest (shortest) train that will work.
It turns out that finding the LCM is extremely easy to model with Cuisenaire Rods using the numbering with the white rod as 1:
a. If the Dark Green Rod is 6, then all trains made of
Dark Green Rods represent numbers that are :
____________________ of 6
Starting Sketch:
b. If the Brown Rod is 8, then all trains made of Brown
Rods represent numbers that are :
____________________ of 8
Starting Sketch:
c. If the Dark Green Rod is 6 and the Brown Rod is 8, then ALL samelength trains that can be made of all Dark Green OR all Brown Rods represent numbers that are :
Starting Sketch:
d. If the Dark Green Rod is 6 and the Brown Rod is 8, then THE SHORTEST samelength trains that can be made of all Dark Green OR all Brown Rods represent the number that is :
Sketch:
e. This train is _____ whites long, therefore _____ is the
LCM of 6 and 8.
At this point you should have trains that look like this on your table .
DARK  GREEN  RODS  DG  
BROWN  RODS  BR 
• Since the white rod is 1, these trains are both 24 whites long and they both represent 24 = LCM (6, 8)
2. As a group , use Cuisenaire Rods and determine the LCM (16, 24). Step out your work and draw welllabeled sketches. What’s One?
3. Suppose that you wish to explain how to find the LEAST COMMON MULTIPLE of two numbers to a student. Using the above steps as a general guide, explain how you would share finding the LCM(4, 6) with a student. Discuss this with your group members and show all of the (completed) steps here.
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