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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 155 · 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.Kabir takes 72 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?
  2. 2.Two tanks hold 200 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Three temple bells ring every 18, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 9, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 6.
  6. 6.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 9 or 3.
  8. 8.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 4, 5 or 8.
  9. 9.Three temple bells ring every 12, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.A hall floor is 60 cm long and 40 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 12, 24 and 10 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 12 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 10 that leaves a remainder of 1 when divided by 5, 8 or 10.
  14. 14.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 30, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 270 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Two tanks hold 360 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Saanvi takes 90 seconds and Ishaan 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?
  19. 19.Three temple bells ring every 8, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Two tanks hold 30 litres and 40 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 40 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 5 or 3.
  23. 23.Two tanks hold 225 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 4, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Arjun takes 36 seconds and Farhan 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?
  27. 27.Two tanks hold 280 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 20, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Arjun takes 50 seconds and Farhan 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?
  30. 30.Three temple bells ring every 9, 4 and 8 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 9 that leaves a remainder of 2 when divided by 9, 8 or 3.
  32. 32.Three temple bells ring every 24, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 180 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 8 or 4.
  35. 35.Two tanks hold 10 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Nisha takes 54 seconds and Manav 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?
  37. 37.Rahul takes 72 seconds and Aarav 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.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 8, 10 or 5.
  39. 39.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Two tanks hold 175 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 216
  2. 40
  3. 72
  4. 72
  5. 26
  6. 12
  7. 38
  8. 43
  9. 60
  10. 6
  11. 120
  12. 60
  13. 41
  14. 24
  15. 60
  16. 30
  17. 40
  18. 180
  19. 40
  20. 10
  21. 10
  22. 46
  23. 25
  24. 60
  25. 24
  26. 360
  27. 40
  28. 60
  29. 450
  30. 72
  31. 74
  32. 120
  33. 45
  34. 26
  35. 5
  36. 270
  37. 216
  38. 42
  39. 20
  40. 25

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