B2.6 Determine the greatest common factor for a variety of whole numbers up to 144 and the lowest common multiple for two and three whole numbers.
Activity 1: Common Place (Lowest Common Multiple)
Materials
- metre stick (or ideally measuring wheel)
- cones
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This activity takes place outside. Place a cone every metre up to about 45 metres (more if needed).
Scenario
To begin, choose 3 students to stand behind the1st cone. Each student moves according to teacher instructions.
Give instructions to all the students in the class concerning the movement of the 3 chosen students.
- The1st student stops at every second cone.
- The2nd stops at every third cone.
- The3rd at every fourth cone.
Ask them which cones the 3 people will stop at.
Note which cones the1st ,2nd and3rdstudent stops at.
- What do you notice?
- Will they stop at a common cone? Explain.
Repeat the exercise, changing the stopping points of the 3 students.
Question again so that students can answer this question:
- How do you predict which is the1st stop (cone) in common? The2nd? What is the1st common stop represent?
Discuss students' strategies.
Additional Activities
Riddle A - Gold Bars
A pirate discovers a treasure chest. In this chest, there are less than 100 gold bars.
- If the pirate divides the gold bars into two equal parts, three equal parts, or five equal parts, there is a
remainder.
If he divides the gold bars into seven equal parts, there is no remainder.
How many bars could there be in the treasure chest? - If the pirate divides the gold bars in the treasure chest:
- into two equal parts, one remains;
- into three equal parts, one remains;
- into five equal parts, one remains;
- into seven equal parts, there is no remainder. Exactly how many gold bars are in the treasure chest?
![](/img/activite/nombres/en/7e/VE7_nombres_Image256_en.png)
Riddle B - Number 1 Song
A new song is all the rage on the radio right now. The song "I Love Life, I Love Math!"
is
topping the charts of several radio stations.
- At the CAC station, this song plays every 30 minutes.
At station CBB, it plays every 24 minutes. At 9:00 a.m., the song played at the same time on both radio stations.
At what time will this happen again? - At 9:00 a.m., CKC was also playing the same song; they play it every 9 minutes.
At what time will the song be played on all three radio stations at the same time?
![](/img/activite/nombres/en/7e/VE7_nombres_Image257_en.png)
Activity 2: Fastest (Greatest Common Factor or GCF)
Materials
- whiteboards
- erasable felt-tip pen
Divide the class into teams of 3. Each student has a whiteboard and a felt-tip pen.
The object of the game is to find the greatest common factor (GCF).
One student writes 2 natural numbers less than 144 on their whiteboard. The other 2 students must use the strategy of their choice to find the GCF. The students share their strategy with each other. Alternate the roles of the team members.
After a few games, add a3rd number.
Review the game as a class, making sure students understand how to find the greatest common factor (GCF). Suggestion: do the activity with the class by projecting 3 numbers on the board.
Variation: Do the same activity with the lowest common multiple (LCM) for 2 or 3 natural numbers.