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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 86 · 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.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Three temple bells ring every 6, 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 15 that leaves a remainder of 1 when divided by 10, 3 or 15.
  4. 4.Two tanks hold 45 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Saanvi takes 75 seconds and Priya 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.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 4 or 8.
  7. 7.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?
  8. 8.Three temple bells ring every 30, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 50 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 4 or 6.
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 10.
  12. 12.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?
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 10 or 5.
  14. 14.Pooja takes 80 seconds and Meera 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?
  15. 15.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?
  16. 16.Priya takes 90 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?
  17. 17.Meera takes 30 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?
  18. 18.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 3 or 6.
  19. 19.Sneha takes 50 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?
  20. 20.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 5 or 6.
  21. 21.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 4 or 6.
  23. 23.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 4, 5 or 3.
  24. 24.Two tanks hold 200 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 4 or 12.
  27. 27.Isha takes 48 seconds and Vivaan 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.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 6 or 15.
  29. 29.Vivaan takes 60 seconds and Aarav 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?
  30. 30.Three temple bells ring every 18, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Isha takes 90 seconds and Rahul 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?
  32. 32.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Rohan 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?
  34. 34.Two tanks hold 400 litres and 350 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 30 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Aarav takes 30 seconds and Farhan 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?
  37. 37.Kavya takes 48 seconds and Aditya 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?
  38. 38.Three temple bells ring every 24, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Manav takes 90 seconds and Meera 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.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 5 or 10.

Answer key

  1. 42
  2. 120
  3. 31
  4. 5
  5. 150
  6. 42
  7. 10
  8. 120
  9. 10
  10. 25
  11. 32
  12. 30
  13. 31
  14. 720
  15. 40
  16. 270
  17. 150
  18. 26
  19. 450
  20. 32
  21. 14
  22. 63
  23. 61
  24. 25
  25. 21
  26. 61
  27. 720
  28. 62
  29. 240
  30. 90
  31. 720
  32. 50
  33. 180
  34. 50
  35. 10
  36. 270
  37. 720
  38. 120
  39. 360
  40. 23

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