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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 14 · 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 5, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Zoya takes 40 seconds and Arjun 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?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 10.
  4. 4.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?
  5. 5.Two tanks hold 75 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Three temple bells ring every 8, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 200 litres and 75 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 18, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 225 litres and 135 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 12 that leaves a remainder of 2 when divided by 12, 3 or 4.
  11. 11.Two tanks hold 50 litres and 80 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 35 litres and 30 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 15 that leaves a remainder of 1 when divided by 4, 12 or 15.
  14. 14.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?
  15. 15.Three temple bells ring every 24, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 18, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Two tanks hold 120 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Two tanks hold 100 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Two tanks hold 20 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Priya takes 30 seconds and Rohan 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?
  21. 21.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?
  22. 22.Isha takes 50 seconds and Tara 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?
  23. 23.Three temple bells ring every 6, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 15, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 9 or 4.
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 10.
  27. 27.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Karan takes 90 seconds and Saanvi 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?
  29. 29.Three temple bells ring every 6, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 3.
  31. 31.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 6 or 5.
  32. 32.Two tanks hold 200 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Two tanks hold 140 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.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 9, 5 or 10.
  36. 36.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 9 or 5.
  37. 37.Tara takes 30 seconds and Saanvi 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.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Two tanks hold 250 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Three temple bells ring every 18, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 60
  2. 360
  3. 61
  4. 40
  5. 15
  6. 120
  7. 25
  8. 72
  9. 45
  10. 14
  11. 10
  12. 5
  13. 61
  14. 35
  15. 120
  16. 90
  17. 20
  18. 50
  19. 5
  20. 150
  21. 24
  22. 400
  23. 30
  24. 30
  25. 38
  26. 31
  27. 21
  28. 270
  29. 60
  30. 17
  31. 121
  32. 40
  33. 15
  34. 20
  35. 94
  36. 183
  37. 270
  38. 20
  39. 50
  40. 90

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