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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 266 · 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 12, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 15, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 6, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Three temple bells ring every 8, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 12, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 100 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Ishaan takes 48 seconds and Saanvi 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?
  10. 10.Arjun takes 40 seconds and Kavya takes 36 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?
  11. 11.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 4.
  13. 13.Two tanks hold 80 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Aarav takes 50 seconds and Tara takes 40 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.Two tanks hold 225 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 9, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Two tanks hold 360 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Ishaan takes 75 seconds and Dev takes 50 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?
  20. 20.Ishaan takes 48 seconds and Nisha takes 90 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?
  21. 21.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Two tanks hold 15 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 5 or 3.
  24. 24.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Three temple bells ring every 4, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Ishaan takes 30 seconds and Sneha 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?
  27. 27.Pooja takes 30 seconds and Tara takes 50 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?
  28. 28.Meera takes 80 seconds and Diya 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?
  29. 29.Three temple bells ring every 10, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 24, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 20, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Manav takes 80 seconds and Nisha takes 36 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 10 that leaves a remainder of 1 when divided by 4, 6 or 10.
  34. 34.Farhan takes 90 seconds and Dev 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?
  35. 35.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Three temple bells ring every 6, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 6.
  38. 38.Two tanks hold 225 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Aarav takes 60 seconds and Saanvi takes 36 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. 24
  2. 120
  3. 90
  4. 14
  5. 120
  6. 60
  7. 25
  8. 6
  9. 432
  10. 360
  11. 21
  12. 62
  13. 20
  14. 35
  15. 200
  16. 45
  17. 72
  18. 45
  19. 150
  20. 720
  21. 50
  22. 5
  23. 31
  24. 21
  25. 72
  26. 240
  27. 150
  28. 720
  29. 60
  30. 120
  31. 120
  32. 720
  33. 61
  34. 360
  35. 42
  36. 90
  37. 31
  38. 25
  39. 14
  40. 180

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