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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 491 · 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.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 6, 10 or 8.
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 10.
  3. 3.Three temple bells ring every 24, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Farhan takes 40 seconds and Saanvi 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?
  5. 5.Two tanks hold 90 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Kavya takes 48 seconds and Meera 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?
  7. 7.Rahul takes 90 seconds and Pooja 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?
  8. 8.Ananya takes 72 seconds and Tara 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?
  9. 9.Rahul takes 60 seconds and Aditya 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?
  10. 10.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 3 or 8.
  11. 11.Three temple bells ring every 8, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 5, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 10 or 3.
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 6 or 4.
  15. 15.A hall floor is 225 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Two tanks hold 25 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Three temple bells ring every 5, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.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?
  20. 20.Two tanks hold 225 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.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?
  22. 22.Manav takes 30 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?
  23. 23.Pooja takes 48 seconds and Vivaan 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?
  24. 24.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 6.
  25. 25.Three temple bells ring every 15, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 8 or 3.
  27. 27.Rohan takes 48 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?
  28. 28.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?
  29. 29.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 10 or 15.
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 6 or 4.
  31. 31.Three temple bells ring every 9, 30 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.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?
  33. 33.Three temple bells ring every 8, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Isha takes 50 seconds and Tara 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?
  35. 35.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?
  36. 36.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Three temple bells ring every 4, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 9, 10 or 6.
  39. 39.Two tanks hold 50 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Two tanks hold 280 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 123
  2. 33
  3. 120
  4. 360
  5. 45
  6. 240
  7. 720
  8. 360
  9. 300
  10. 25
  11. 120
  12. 60
  13. 31
  14. 15
  15. 20
  16. 5
  17. 56
  18. 120
  19. 10
  20. 45
  21. 15
  22. 150
  23. 720
  24. 20
  25. 90
  26. 121
  27. 240
  28. 120
  29. 31
  30. 61
  31. 90
  32. 45
  33. 24
  34. 150
  35. 21
  36. 20
  37. 60
  38. 92
  39. 25
  40. 40

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