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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 375 · 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.Two tanks hold 90 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Zoya takes 36 seconds and Priya 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?
  3. 3.Tara takes 30 seconds and Priya 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?
  4. 4.Ananya takes 45 seconds and Dev 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?
  5. 5.Two tanks hold 210 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Farhan takes 45 seconds and Aditya 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?
  7. 7.Two tanks hold 75 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Farhan takes 54 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?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 12, 9 or 15.
  10. 10.Two tanks hold 35 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 10.
  12. 12.Three temple bells ring every 10, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.A hall floor is 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Two tanks hold 45 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 6 or 15.
  16. 16.Three temple bells ring every 10, 15 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 10 or 3.
  18. 18.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 8, 4 or 6.
  21. 21.Two tanks hold 25 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.A hall floor is 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Three temple bells ring every 6, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 150 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Two tanks hold 45 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Two tanks hold 100 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Aarav takes 30 seconds and Isha 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?
  28. 28.Three temple bells ring every 15, 10 and 6 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 10 that leaves a remainder of 1 when divided by 4, 3 or 10.
  30. 30.Three temple bells ring every 6, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Ananya takes 48 seconds and Meera 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?
  32. 32.Find the smallest number bigger than 10 that leaves a remainder of 5 when divided by 9, 10 or 6.
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 6.
  34. 34.Vivaan takes 30 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?
  35. 35.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?
  36. 36.Three temple bells ring every 10, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 20 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Saanvi takes 30 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?
  39. 39.Two tanks hold 45 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Rahul takes 30 seconds and Sneha 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?

Answer key

  1. 10
  2. 360
  3. 270
  4. 270
  5. 30
  6. 180
  7. 25
  8. 216
  9. 184
  10. 5
  11. 61
  12. 120
  13. 30
  14. 5
  15. 32
  16. 90
  17. 32
  18. 6
  19. 20
  20. 27
  21. 5
  22. 35
  23. 30
  24. 30
  25. 15
  26. 20
  27. 150
  28. 30
  29. 61
  30. 120
  31. 144
  32. 95
  33. 31
  34. 360
  35. 10
  36. 60
  37. 10
  38. 90
  39. 5
  40. 90

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