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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 54 · 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 6, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 75 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Two tanks hold 120 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.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?
  5. 5.Two tanks hold 35 litres and 40 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 15 that leaves a remainder of 1 when divided by 3, 8 or 15.
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 15, 10 or 9.
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 5 or 12.
  9. 9.Two tanks hold 160 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.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?
  11. 11.Two tanks hold 280 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Three temple bells ring every 12, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Three temple bells ring every 20, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Three temple bells ring every 4, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Meera takes 75 seconds and Kavya takes 30 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.Three temple bells ring every 30, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 270 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Kavya takes 45 seconds and Aarav 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?
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 4 or 15.
  22. 22.Three temple bells ring every 15, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 10 or 3.
  24. 24.Nisha takes 60 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?
  25. 25.Two tanks hold 160 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Meera takes 45 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?
  27. 27.Three temple bells ring every 12, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 20, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 24, 15 and 4 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 12 that leaves a remainder of 2 when divided by 3, 12 or 8.
  31. 31.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 5 or 3.
  32. 32.Three temple bells ring every 15, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 75 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Three temple bells ring every 10, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 6, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 240 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Farhan takes 48 seconds and Zoya 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?
  38. 38.Two tanks hold 180 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 8 or 15.
  40. 40.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?

Answer key

  1. 30
  2. 15
  3. 40
  4. 20
  5. 5
  6. 121
  7. 96
  8. 61
  9. 20
  10. 40
  11. 40
  12. 72
  13. 10
  14. 60
  15. 42
  16. 60
  17. 150
  18. 90
  19. 30
  20. 180
  21. 62
  22. 60
  23. 32
  24. 180
  25. 20
  26. 450
  27. 36
  28. 40
  29. 120
  30. 26
  31. 122
  32. 120
  33. 25
  34. 120
  35. 120
  36. 30
  37. 144
  38. 45
  39. 121
  40. 15

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