Question 1: Find the Least Common Multiple (LCM) of 6 and 8. Show your working.

Answer: 24

Question 2: Calculate the LCM of 9 and 12.

Answer: 36

Question 3: Identify the mistake in the following: The student states that the LCM of 10 and 15 is 25 because they added the two numbers. Correct the mistake.

Answer: The student should find the smallest number divisible by both 10 and 15, which is 30, not 25. They added instead of finding the LCM.

Question 4: Using the grid, construct the smallest common multiple of 4 and 5.

Answer: 20

Question 5: Find the LCM of 7 and 14. Show your working.

Answer: 14

Question 6: A student claims that the LCM of 8 and 12 is 24 because 8 × 3 = 24. Is this always correct? Justify your answer.

Answer: No, because LCM is the smallest multiple common to both. For 8 and 12, the LCM is 24, but the student’s reasoning of multiplying 8 by 3 only works when 8 divides 24 evenly. The correct method is to find the smallest multiple they share.

Question 7: Calculate the LCM of 18 and 24. Use prime factorization.

Answer: 72

Question 8: Explain why the LCM of 5 and 10 is 10, not 15 or 20.

Answer: Because 10 is the smallest number divisible by both 5 and 10, while 15 and 20 are larger multiples and not the smallest.

Question 9: Find the LCM of 25 and 30 and show your work.

Answer: 150

Question 10: A problem in a factory requires parts to be assembled in batches. If parts are produced in batches of 6 and 9, what is the smallest batch size that can be used to produce both types of parts together? Find the LCM.

Answer: 18

Question 11: A student incorrectly states that the LCM of 12 and 18 is 36 because they multiplied the two numbers. Correct this misconception by finding the actual LCM and explaining the mistake.

Answer: The correct LCM of 12 and 18 is 36, but the student’s reasoning is flawed because they multiplied the numbers without finding the smallest common multiple. Proper method involves listing multiples or prime factorization.