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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 285 · 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.Zoya takes 50 seconds and Manav 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?
  2. 2.Two tanks hold 150 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Three temple bells ring every 6, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 5, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Ananya takes 36 seconds and Manav 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?
  7. 7.Pooja takes 75 seconds and Tara 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?
  8. 8.Ananya takes 36 seconds and Aarav 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?
  9. 9.Ishaan takes 36 seconds and Meera 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.Two tanks hold 405 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Two tanks hold 60 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Kabir takes 40 seconds and Saanvi 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?
  15. 15.Karan takes 48 seconds and Ananya 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.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 8 or 15.
  17. 17.Three temple bells ring every 8, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 4, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 15, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 4 or 5.
  21. 21.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 3 or 6.
  22. 22.Two tanks hold 30 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Two tanks hold 210 litres and 60 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 24, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Nisha takes 36 seconds and Meera 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?
  26. 26.Three temple bells ring every 6, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 10 or 3.
  28. 28.Manav takes 50 seconds and Sneha 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?
  29. 29.Three temple bells ring every 4, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Vivaan takes 30 seconds and Zoya 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?
  31. 31.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Saanvi takes 30 seconds and Karan 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?
  33. 33.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Two tanks hold 35 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Two tanks hold 270 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 8, 12 or 6.
  38. 38.Vivaan 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?
  39. 39.Three temple bells ring every 12, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Two tanks hold 35 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 400
  2. 50
  3. 120
  4. 40
  5. 21
  6. 720
  7. 225
  8. 360
  9. 108
  10. 45
  11. 12
  12. 10
  13. 10
  14. 360
  15. 240
  16. 121
  17. 120
  18. 120
  19. 60
  20. 23
  21. 26
  22. 15
  23. 30
  24. 72
  25. 180
  26. 24
  27. 32
  28. 150
  29. 72
  30. 150
  31. 56
  32. 360
  33. 42
  34. 5
  35. 45
  36. 30
  37. 28
  38. 120
  39. 60
  40. 5

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