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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 494 · 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 8, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Kabir takes 75 seconds and Isha 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?
  3. 3.Two tanks hold 315 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 9 or 8.
  5. 5.Farhan takes 80 seconds and Rahul 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?
  6. 6.Two tanks hold 150 litres and 90 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 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?
  8. 8.Three temple bells ring every 8, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Saanvi 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?
  10. 10.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Three temple bells ring every 6, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 5.
  13. 13.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 4.
  14. 14.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.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?
  16. 16.Rohan takes 48 seconds and Arjun 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?
  17. 17.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 3 or 10.
  18. 18.Three temple bells ring every 6, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Pooja takes 40 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?
  20. 20.Two tanks hold 120 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Ishaan takes 36 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?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 3 or 15.
  23. 23.Two tanks hold 360 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 5 or 15.
  25. 25.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 10, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Farhan takes 50 seconds and Rahul 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?
  28. 28.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Two tanks hold 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.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?
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 7 when divided by 12, 8 or 10.
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 5.
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 10.
  34. 34.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 4 or 3.
  35. 35.Saanvi takes 75 seconds and Rohan 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?
  36. 36.Two tanks hold 120 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Meera takes 30 seconds and Tara 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?
  38. 38.Farhan takes 40 seconds and Rahul 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?
  39. 39.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 3 or 10.
  40. 40.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?

Answer key

  1. 72
  2. 150
  3. 45
  4. 74
  5. 400
  6. 30
  7. 10
  8. 120
  9. 540
  10. 28
  11. 90
  12. 61
  13. 62
  14. 15
  15. 21
  16. 240
  17. 32
  18. 120
  19. 360
  20. 40
  21. 360
  22. 122
  23. 45
  24. 16
  25. 24
  26. 90
  27. 450
  28. 10
  29. 10
  30. 120
  31. 127
  32. 62
  33. 32
  34. 13
  35. 150
  36. 15
  37. 270
  38. 360
  39. 61
  40. 30

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