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 6 and 8.

Answer: 24

Question 3: Find the first three common multiples of 5 and 7.

Answer: 35, 70, 105

Question 4: Determine whether 48 is a common multiple of 6 and 8. Show your reasoning.

Answer: Yes, because 48 ÷ 6 = 8 and 48 ÷ 8 = 6, both are integers.

Question 5: Plot the multiples of 3 and 4 on the grid below to find their common multiples up to 60.

Answer:

Question 6: A bus arrives every 12 minutes, and a train arrives every 15 minutes. When will they arrive together again after 8:00 am? (Calculate the time in minutes after 8:00 am.)

Answer: 60 minutes

Question 7: Construct a triangle with sides that are multiples of 4 and 6, where the sides have a common multiple of 24. Label the sides.

Answer:

Question 8: Identify the mistake in this reasoning: 'Since 36 is divisible by 4 and 6, it must be the least common multiple of 4 and 6.'

Answer: The mistake is assuming 36 is the least common multiple without checking smaller common multiples. The actual LCM of 4 and 6 is 12.

Question 9: Find all common multiples of 9 and 12 less than 100.

Answer: 36, 72

Question 10: A factory produces widgets every 18 minutes, and gadgets every 24 minutes. How often do they produce both together? (Express in minutes.)

Answer: 216 minutes