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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 345 · 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 24, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 225 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Zoya takes 50 seconds and Diya 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?
  4. 4.A hall floor is 225 cm long and 135 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 5, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Two tanks hold 180 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.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?
  8. 8.Two tanks hold 225 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Two tanks hold 150 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Three temple bells ring every 12, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.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?
  12. 12.Pooja takes 36 seconds and Aarav 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?
  13. 13.Three temple bells ring every 6, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.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?
  15. 15.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 6 or 8.
  16. 16.Pooja takes 72 seconds and Farhan 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.Two tanks hold 210 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Nisha takes 60 seconds and Ananya 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?
  19. 19.Two tanks hold 30 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.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?
  21. 21.Two tanks hold 10 litres and 45 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 24, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 6, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Vivaan takes 54 seconds and Aarav 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?
  25. 25.Two tanks hold 50 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Manav takes 72 seconds and Diya 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?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 3 or 15.
  28. 28.Manav takes 60 seconds and Kabir 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?
  29. 29.Three temple bells ring every 6, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 6, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 4, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Rohan takes 80 seconds and Kabir 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?
  33. 33.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 6 or 9.
  36. 36.Ishaan takes 40 seconds and Meera 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?
  37. 37.Two tanks hold 140 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.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?
  39. 39.A hall floor is 300 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Ishaan takes 48 seconds and Vivaan 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?

Answer key

  1. 120
  2. 25
  3. 150
  4. 15
  5. 60
  6. 45
  7. 21
  8. 45
  9. 30
  10. 24
  11. 50
  12. 180
  13. 60
  14. 120
  15. 25
  16. 360
  17. 30
  18. 300
  19. 15
  20. 21
  21. 5
  22. 72
  23. 90
  24. 432
  25. 10
  26. 360
  27. 16
  28. 240
  29. 120
  30. 60
  31. 72
  32. 240
  33. 12
  34. 24
  35. 73
  36. 120
  37. 20
  38. 30
  39. 30
  40. 240

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