Prime Factor Method: Error Analysis & Misconceptions
Mathematics
Grade 7
12 questions
~24 mins
1 views0 downloads
About This Worksheet
This worksheet explores the Prime Factor Method for calculating the Lowest Common Multiple (LCM), focusing on identifying common mistakes and misconceptions. It includes fluency, problem-solving, real-world applications, and extension questions designed for Grade 7 students.
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Prime Factor Method: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Answer all questions clearly. Show your working steps in the provided grids.
1.
Find the prime factorization of 36.
[2 marks]2.
Calculate the LCM of 12 and 15 using the Prime Factor Method.
[3 marks]3.
Prime factorize 48 and 180. Identify the highest powers of each prime used in both.
[3 marks]B
Problem Solving & Reasoning
Work through the problems step-by-step. Explain your reasoning where necessary.
1.
A school bus departs every 15 minutes, and a train arrives every 20 minutes. How often will both arrive at the station at the same time? Use the Prime Factor Method to find the LCM of 15 and 20.
[4 marks]2.
Explain why simply multiplying the prime factorizations of two numbers does not always give the LCM. Give an example.
[4 marks]3.
Two gears rotate such that one completes a full rotation every 12 seconds and the other every 18 seconds. What is the time in seconds when both gears rotate together again? Use prime factorization to find your answer.
[3 marks]C
Real-world Applications
Apply the Prime Factor Method to solve these practical problems.
1.
A gardener waters flowers every 8 days, and another gardener waters every 12 days. When will they water the flowers together again?
[3 marks]2.
A factory produces products in batches of 24 and 36 units. After how many units will both machines finish a batch at the same time? Use prime factorization.
[3 marks]D
Challenge & Extension
Attempt these advanced problems to deepen your understanding.
1.
Find the LCM of 84, 126, and 210 using the Prime Factor Method. Show all steps.
[4 marks]2.
A set of three tasks repeats every 20, 30, and 45 minutes respectively. When will all three tasks start simultaneously again? Explain your solution using prime factorization.
[4 marks]E
Mixed Review & Error Analysis
Identify and correct the mistakes in the following student solutions.
1.
A student finds the prime factorization of 48 as 2^4 and 180 as 2^2 * 3^2, then incorrectly multiplies these to find the LCM as 2^4 * 3^2 = 144. Explain and correct the mistake.
[3 marks]2.
A student calculates the LCM of 8 and 12 as 24 by taking 2^3 and 2^2*3, then multiplying 2^3 * 3 = 24. Is this correct? Why or why not?
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
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- • Add more questions (10 → 15)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet