Question 1: Find the Least Common Multiple (LCM) of 8 and 12.

Answer: 24

Question 2: Calculate the LCM of 15 and 20.

Answer: 60

Question 3: What is the LCM of 9 and 14?

Answer: 126

Question 4: Construct a triangle on the grid with sides of lengths 6 and 8, and find a possible third side length that makes the triangle possible, based on LCM.

Answer: The third side can be 24 or any multiple of 8 and 6 (e.g., 24).

Question 5: Find the LCM of 18 and 24.

Answer: 72

Question 6: Add the fractions 3/8 and 5/12. Show your working by first finding the LCM of the denominators.

Answer: LCM of 8 and 12 is 24; 3/8 = 9/24, 5/12 = 10/24; sum = 19/24

Question 7: Solve: 7/9 + 4/15. Show your working.

Answer: LCM of 9 and 15 is 45; 7/9 = 35/45, 4/15 = 12/45; sum = 47/45

Question 8: A recipe requires 1/6 cup of sugar and 1/8 cup of flour. Find the smallest amount of combined mixture so that both ingredients can be measured exactly, using the LCM of the denominators.

Answer: LCM of 6 and 8 is 24; 1/6 = 4/24, 1/8 = 3/24; total = 7/24 cups

Question 9: Identify and correct the mistake: Find the LCM of 10 and 15 is 25.

Answer: Incorrect. The LCM of 10 and 15 is 30, not 25.

Question 10: Calculate the LCM of 21 and 28, then add the fractions 2/21 and 3/28.

Answer: LCM of 21 and 28 is 84; 2/21 = 8/84, 3/28 = 9/84; sum = 17/84

Question 11: Find two numbers between 1 and 50 whose LCM is 120. Show reasoning.

Answer: Examples include 10 and 12, since LCM(10,12)=60; need larger numbers. For 24 and 30, LCM=120.

Question 12: Challenge: Find the LCM of 36 and 48, then determine the sum of their multiples up to 120.

Answer: LCM of 36 and 48 is 144; multiples up to 120 are 36, 48, 72, 96, but 144 exceeds 120.