Question 1: List the first five common multiples of 3 and 4.

Answer: 12, 24, 36, 48, 60

Question 2: Calculate the least common multiple (LCM) of 8 and 12.

Answer: 24

Question 3: Identify the first three common multiples of 5 and 6.

Answer: 30, 60, 90

Question 4: Plot the graph of y = 2x for x values from 1 to 10.

Answer: Plot points at (1,2), (2,4), (3,6), (4,8), (5,10), (6,12), (7,14), (8,16), (9,18), (10,20).

Question 5: Explain why 45 is not a common multiple of 4 and 6.

Answer: Because 45 is not divisible by 4 or 6 without a remainder, so it is not a multiple of either.

Question 6: Find the first common multiple of 7 and 9 that is greater than 50.

Answer: 63

Question 7: A factory produces items every 6 days and maintenance occurs every 8 days. When will both events occur on the same day again?

Answer: The least common multiple of 6 and 8 is 24 days, so they occur together every 24 days.

Question 8: Identify the error: A student finds the common multiples of 3 and 5 as 15, 30, 45, 60, 75. Is this correct? If not, correct the list.

Answer: Incorrect. The common multiples are 15, 30, 45, 60, 75, 90, etc. But 45 is a multiple of both 3 and 5, so the list is correct. No error.

Question 9: Construct a number line on the grid and mark the first four common multiples of 4 and 7.

Answer: Mark 28, 56, 84, 112 on the number line.

Question 10: Find the least common multiple of 9 and 14. Show your working.

Answer: Prime factors: 9=3^2, 14=2×7; LCM=2×3^2×7=126.

Question 11: Which of the following pairs have the same least common multiple? a) 6 and 8, b) 9 and 12, c) 10 and 15. Justify your choice.

Answer: Pairs a) 6 and 8 have LCM 24. Pair b) 9 and 12 also have LCM 36. Pair c) 10 and 15 have LCM 30. So, pairs a) and b) have the same LCM.

Question 12: Identify a common multiple of 12 and 15 that is less than 100. Explain how you found it.

Answer: 60. Found by listing multiples of 12 (12, 24, 36, 48, 60, ...) and 15 (15, 30, 45, 60, ...).