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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 323 · 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 4, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 180 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Priya takes 45 seconds and Ishaan 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?
  4. 4.Priya takes 72 seconds and Isha 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?
  5. 5.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 5 or 3.
  6. 6.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?
  7. 7.Two tanks hold 105 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Three temple bells ring every 5, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Manav takes 45 seconds and Rahul 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?
  10. 10.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 6.
  12. 12.Two tanks hold 100 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 9 or 3.
  14. 14.Three temple bells ring every 10, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Isha takes 36 seconds and Rohan 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?
  16. 16.Two tanks hold 10 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Priya takes 60 seconds and Rohan 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?
  18. 18.Kabir takes 36 seconds and Priya 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?
  19. 19.Rahul takes 60 seconds and Isha 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?
  20. 20.Vivaan takes 30 seconds and Rahul takes 48 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.Three temple bells ring every 4, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Two tanks hold 80 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Three temple bells ring every 8, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.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?
  25. 25.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Two tanks hold 105 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Two tanks hold 75 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 10 or 3.
  29. 29.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 4, 3 or 5.
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 8, 15 or 10.
  32. 32.Three temple bells ring every 5, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Vivaan takes 40 seconds and Tara 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?
  34. 34.Vivaan takes 45 seconds and Saanvi 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?
  35. 35.Three temple bells ring every 20, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 6, 10 and 18 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 9 that leaves a remainder of 1 when divided by 3, 9 or 8.
  38. 38.Three temple bells ring every 24, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Two tanks hold 120 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 12 or 15.

Answer key

  1. 36
  2. 45
  3. 360
  4. 720
  5. 121
  6. 15
  7. 15
  8. 120
  9. 180
  10. 42
  11. 32
  12. 25
  13. 73
  14. 90
  15. 180
  16. 5
  17. 120
  18. 180
  19. 540
  20. 240
  21. 60
  22. 40
  23. 120
  24. 35
  25. 12
  26. 15
  27. 25
  28. 31
  29. 21
  30. 61
  31. 123
  32. 60
  33. 360
  34. 450
  35. 60
  36. 90
  37. 73
  38. 120
  39. 30
  40. 61

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