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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 67 · 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.Farhan takes 48 seconds and Karan 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?
  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.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 10 or 4.
  4. 4.Three temple bells ring every 5, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Rohan takes 72 seconds and Sneha 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?
  6. 6.Three temple bells ring every 10, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 10, 15 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 6 or 4.
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 15 or 6.
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 8, 15 or 6.
  11. 11.A hall floor is 320 cm long and 280 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 12 that leaves a remainder of 1 when divided by 5, 3 or 12.
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 6, 9 or 5.
  14. 14.Two tanks hold 50 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Karan takes 30 seconds and Nisha 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?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 3.
  18. 18.Sneha takes 72 seconds and Arjun 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.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 3 or 8.
  20. 20.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Two tanks hold 40 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Three temple bells ring every 12, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 6 or 10.
  24. 24.Two tanks hold 15 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 24, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 75 litres and 105 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 90 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Two tanks hold 120 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Pooja takes 45 seconds and Diya takes 75 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?
  30. 30.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 12 or 5.
  31. 31.Arjun takes 54 seconds and Saanvi 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?
  32. 32.Two tanks hold 120 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 8.
  34. 34.Two tanks hold 40 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Priya takes 40 seconds and Karan takes 75 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?
  38. 38.Three temple bells ring every 24, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Rohan 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?
  40. 40.Three temple bells ring every 30, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 432
  2. 120
  3. 62
  4. 40
  5. 360
  6. 120
  7. 90
  8. 13
  9. 61
  10. 121
  11. 56
  12. 61
  13. 93
  14. 10
  15. 28
  16. 90
  17. 61
  18. 360
  19. 25
  20. 35
  21. 10
  22. 120
  23. 31
  24. 5
  25. 120
  26. 15
  27. 30
  28. 15
  29. 225
  30. 121
  31. 432
  32. 40
  33. 25
  34. 10
  35. 42
  36. 24
  37. 600
  38. 72
  39. 360
  40. 90

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