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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 513 · 40 questions
TalentJR

The method (LCM or HCF?): Bells, lights, runners “together again”: find the LCM of the gaps. Biggest can, rope piece or tile that fits exactly: find the HCF. Leaves the same remainder r every time: LCM + r. Number of tiles = (length ÷ tile side) × (width ÷ tile side).

NameDateTime takenScore ___ / 40
  1. 1.Three temple bells ring every 8, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 135 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Two tanks hold 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Rohan takes 54 seconds and Kavya takes 72 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  5. 5.Two tanks hold 240 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Three temple bells ring every 4, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 25 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Rahul takes 48 seconds and Vivaan takes 80 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  9. 9.Three temple bells ring every 10, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 300 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Two tanks hold 20 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Three temple bells ring every 8, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Vivaan takes 36 seconds and Priya takes 30 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  14. 14.Two tanks hold 315 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Ananya takes 30 seconds and Arjun takes 54 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  16. 16.Saanvi takes 40 seconds and Ananya takes 60 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  17. 17.Saanvi takes 40 seconds and Dev takes 60 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  18. 18.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 8, 4 or 9.
  19. 19.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Three temple bells ring every 8, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 12, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Two tanks hold 30 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 20, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 12 or 9.
  28. 28.Three temple bells ring every 20, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Three temple bells ring every 20, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Karan takes 60 seconds and Priya takes 80 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  33. 33.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 10, 8 or 12.
  34. 34.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 6, 5 or 4.
  35. 35.Two tanks hold 280 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 5.
  37. 37.Three temple bells ring every 24, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Two tanks hold 225 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 6, 9 or 12.
  40. 40.Kabir takes 30 seconds and Rohan takes 45 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?

Answer key

  1. 120
  2. 15
  3. 20
  4. 216
  5. 40
  6. 60
  7. 5
  8. 240
  9. 120
  10. 50
  11. 10
  12. 72
  13. 180
  14. 45
  15. 270
  16. 120
  17. 120
  18. 74
  19. 30
  20. 72
  21. 60
  22. 6
  23. 15
  24. 60
  25. 10
  26. 28
  27. 37
  28. 60
  29. 15
  30. 40
  31. 42
  32. 240
  33. 122
  34. 62
  35. 40
  36. 61
  37. 120
  38. 25
  39. 39
  40. 90

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