Lesson: LCM

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Lesson Objective

SWBAT find the least common multiple for any set of numbers

Lesson Plan

Lesson Steps: Thursday

Do Now-10min

Teacher circulates and checks home work/stamps do now sheets as students complete the four do now problems.  After five minutes call on students to answer question and review any misconceptions.

HW Check- 6 min

·         Check All – put up all answers on whiteboard

·         Students check all problems on homework (3 minutes – 1 minute front, 1 minute back)

·         Teacher walks around while students are checking work to intervene.

·         Teacher identifies the one or two most common mistakes on homework and reviews it whole class on transparency.  (1 – 2 minutes)  Before review – ask students to think about the steps I am taking while I solve the problem(s) – they will share whole class afterwards.

Paper Pass in Transition:


Mental Math: 5min  

·         Teacher reads and shows problem

·         Student pulls a stick to call on student to answer

·         Last problem string – all students complete and answer by raising hand – fastest hand called on


Transition:  (Assigning responsible dollars for students on task, i.e. notes out, desk cleared)


Mini-Lesson: (30 mins)

§  Launch:

o     Let’s start today by playing the guessing game.  I am thinking of a number.  3 is a factor of my number and 4 is a factor of my number.  What number could I have in mind:  12, 24 and so on.   Allow students to use calculators – punch in a number that can be divided by 3 and divided by 4. 

o    How many other numbers would work?  Lots, more than we can count and infinite number.

o    What numbers have 3 as a factor?  3, 6, 9, 12, 15…

o    What do we call these numbers?  Multiples of 3

o    What numbers have 4 as a factor?  4, 8, 12, 16, 20…

o    What do we call these numbers? Multiples of 4

o    Which numbers are in both sets?  12, 24, 36, ….

o    What do we call these numbers?  Numbers that are multiples of 3 and of 4.

o    We can also call these COMMON MULTIPLES of 3 and 4.   Define the word common multiples on NOTES page.

o    Is 48 a common multiple of 3 and 4?  Yes because 3 x 16 = 48 and 4 x 12 = 48.

o    Is 92 a common multiple of 3 and 4?   No, 3 is not a factor of 92.

o    Let’s try another guessing game example:  I’m thinking of a number. 6 is a factor of my number and 9 is afacotr of my number.  My number is more than 50 but less than 100.  What is my number?  72, 54 or 90

o    MODEL:  How can you find these numbers?  List the multiples of 9, list the multiples of 6 and see what they have in common? Students take notes on this processs.

§  Explore:

o    Guessing Game:  I’m thking of the SMALLEST number that has both 3 AND 4 as factors? What could the number be?  Ask student to make a list of the multiples of 3 and 4.    Answer:  12

o    Would any other numbers work?  NO, there is only one smallest common multiple.

o    How do you know/ how did you find it?  List multiples of both and look for the SMALLEST one they have in common. 

o    Define LCM – students take notes  (The smallest common multiple or first common multiple of two or more numbers)

o    12 is the LCM of 3 and 4 and 12 = 3 x 4.  Do you think the LCM is always the product of two numbers?  Various answers.

o    Let’s see – let’s try the numbers 6 and 8.  LCM is not 6 x 8.  So it doesn’t always work.

§  Discuss:

o    Why do we even both finding the LCM.  When would we ever do this?  Discuss that we will continue to see why LCM is important for us to know over the next couple of classes, however, one application is to solve problems like the following:

o    Display the Ferris Wheel problem.  When are the wheel’s both at the bottom again?

§  Practice:

o    Students will practice finding the least common multiple for different numbers. 


Lesson Resources

LCM Hw  
lcm reteach  
U4 L6 Notes Prime Time LCM  


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