Question 1: Calculate the smallest common multiple of 4 and 6.

Answer: 12

Question 2: Find the first five common multiples of 3 and 5.

Answer: 15, 30, 45, 60, 75

Question 3: What is the least common multiple (LCM) of 8 and 12?

Answer: 24

Question 4: Plot the graph of y=2x for x values from 0 to 10. (Draw on grid)

Answer: Coordinates will be (0,0), (1,2), (2,4), ..., (10,20)

Question 5: Construct a triangle with sides that are all multiples of 3 and 4, with the smallest possible integer lengths.

Answer: Sides of length 3, 4, and 12

Question 6: A factory produces items every 6 days and a delivery occurs every 9 days. After how many days will both events happen on the same day again?

Answer: 18

Question 7: A bus departs every 15 minutes and a train departs every 20 minutes from the same station. If both leave at the same time, after how many minutes will they leave together again?

Answer: 60

Question 8: Explain why the least common multiple of 9 and 12 is 36. Show your working.

Answer: Prime factors of 9: 3²; of 12: 2²×3. LCM: 2²×3²=36.

Question 9: A printer needs to print pages in batches of 8 or 12. What is the smallest number of pages that can be printed in both batch sizes?

Answer: 24

Question 10: Identify and correct the mistake: The common multiples of 4 and 6 are 10, 14, 20, 24. Why is this incorrect?

Answer: Incorrect multiples listed; they are not multiples of both 4 and 6; common multiples are 12, 24, etc.

Question 11: A beauty salon offers appointments every 7 days and every 10 days. When will both types of appointments be available on the same day again? Show your working.

Answer: 70