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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 328 · 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 10, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 10 or 8.
  3. 3.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 5 or 8.
  4. 4.Arjun takes 45 seconds and Ananya 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?
  5. 5.Two tanks hold 180 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 9 or 10.
  7. 7.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 4 or 5.
  8. 8.Manav takes 48 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?
  9. 9.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 4 or 5.
  10. 10.Two tanks hold 100 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Two tanks hold 120 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 350 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Two tanks hold 75 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.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?
  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.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?
  17. 17.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?
  18. 18.Farhan takes 80 seconds and Sneha 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?
  19. 19.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?
  20. 20.Two tanks hold 40 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 8 or 10.
  22. 22.Three temple bells ring every 4, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Pooja takes 60 seconds and Ananya 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?
  24. 24.Tara takes 45 seconds and Aarav 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?
  25. 25.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Two tanks hold 75 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 15, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 15, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 10, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.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?
  31. 31.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?
  32. 32.Three temple bells ring every 30, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 9, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 90 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.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?
  36. 36.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Tara takes 75 seconds and Kabir 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?
  39. 39.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?
  40. 40.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?

Answer key

  1. 30
  2. 122
  3. 121
  4. 360
  5. 20
  6. 91
  7. 23
  8. 720
  9. 22
  10. 50
  11. 20
  12. 50
  13. 25
  14. 25
  15. 20
  16. 21
  17. 5
  18. 720
  19. 5
  20. 5
  21. 43
  22. 24
  23. 120
  24. 180
  25. 42
  26. 15
  27. 30
  28. 60
  29. 40
  30. 42
  31. 120
  32. 60
  33. 90
  34. 30
  35. 24
  36. 20
  37. 14
  38. 150
  39. 10
  40. 5

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