Question 1: Find the least common multiple (LCM) of 12 and 18. Use prime factorisation.

Answer: 36

Question 2: Calculate the LCM of 8, 12, and 20.

Answer: 120

Question 3: Add the fractions 3/12 and 5/18. Show your working.

Answer: Calculate LCM of 12 and 18 = 36. Convert fractions: 3/12 = 9/36, 5/18=10/36. Sum = 19/36.

Question 4: Simplify the sum of 7/8 and 3/10. Show your working.

Answer: LCM of 8 and 10 = 40. Convert: 7/8=35/40, 3/10=12/40. Sum=47/40 or 1 7/40.

Question 1: A recipe requires 2/3 cup of sugar and 3/4 cup of flour. To prepare a larger batch, you want to find the smallest amount of mixture where both ingredients can be evenly scaled. How much sugar and flour are in this mixture? Show your working.

Answer: LCM of 3 and 4 = 12. For sugar: 2/3 = 8/12; for flour: 3/4=9/12. So, smallest equal amount is 8/12 cup sugar and 9/12 cup flour.

Question 2: Two trains leave different stations heading towards each other. Train A departs every 6 minutes, and Train B every 8 minutes. After how many minutes will both trains depart simultaneously from their stations again? Explain your calculation.

Answer: LCM of 6 and 8 = 24 minutes. Both will depart together every 24 minutes.

Question 3: A gardener waters two sections of a garden. One section needs watering every 12 days, and the other every 15 days. When is the next day both sections will need watering on the same day? Show your working.

Answer: LCM of 12 and 15 = 60 days. Next simultaneous watering after 60 days.

Question 4: Construct two fractions with denominators that require finding a complex LCM to add. The fractions are 5/24 and 7/36. Show the addition process.

Answer: LCM of 24 and 36 = 72. Convert: 5/24=15/72, 7/36=14/72. Sum=29/72.

Question 1: A cyclist rides 3/8 of a mile every 10 minutes, and another rides 2/5 of a mile every 12 minutes. After how long will they have traveled the same distance? Show your working.

Answer: LCM of 10 and 12 = 60 minutes. Distance for first: (3/8) × 6= 9/4 miles, second: (2/5) × 5= 2 miles. Find equal distance: 9/4 miles = 2.25 miles, approximate to find common time.

Question 2: A factory produces 5/16 ton of product each day, and another produces 3/10 ton. When will their total weekly production be equal? Show your calculations.

Answer: LCM of 16 and 10 = 80. For first: (5/16)×5=25/16, second: (3/10)×8=24/10. Equal total production at least common multiple days.

Question 1: Find the sum of 7/45 and 11/60. Then, express the result as a mixed number if appropriate.

Answer: LCM of 45 and 60 = 180. Convert: 7/45=28/180, 11/60=33/180. Sum=61/180, simplified if needed.

Question 2: Two fractions 9/40 and 7/48 need to be added. Find their LCM and complete the addition.

Answer: LCM of 40 and 48 = 240. Convert: 9/40=54/240, 7/48=35/240. Sum=89/240.

Question 1: Add 4/15 and 7/20. Show your working and provide the simplified answer.

Answer: LCM of 15 and 20 = 60. Convert: 4/15=16/60, 7/20=21/60. Sum=37/60.

Question 2: Find the LCM of 14, 35, and 50 and use it to add 1/14, 2/35, and 3/50.

Answer: LCM of 14, 35, 50 = 700. Convert: 1/14=50/700, 2/35=40/700, 3/50=42/700. Sum=132/700 or simplified.

Question 1: Student claims: The LCM of 8 and 12 is 24. Correct their mistake and find the actual LCM.

Answer: Incorrect. The prime factorisation shows: 8=2^3, 12=2^2×3. LCM=2^3×3=24, which is correct. But if they made a mistake, it might be in calculation; correct LCM is 24.

Question 2: A student adds fractions 3/10 and 4/15 and gets 7/25. Explain the error and provide the correct sum.

Answer: Incorrect. LCM of 10 and 15=30. Convert: 3/10=9/30, 4/15=8/30. Sum=17/30.