# 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 same-length 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 same-length 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 well -labeled 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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