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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 421 · 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.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 5 or 9.
  2. 2.Two tanks hold 60 litres and 70 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 20, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Ananya takes 54 seconds and Isha 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?
  5. 5.Kavya takes 90 seconds and Kabir 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?
  6. 6.Three temple bells ring every 5, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 3 or 10.
  8. 8.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?
  9. 9.Two tanks hold 135 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Meera takes 45 seconds and Zoya 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?
  11. 11.Nisha takes 30 seconds and Rohan 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?
  12. 12.Two tanks hold 40 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 8, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Two tanks hold 15 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Two tanks hold 120 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Two tanks hold 60 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 8, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 12 or 9.
  20. 20.Arjun takes 54 seconds and Nisha 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?
  21. 21.Three temple bells ring every 30, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Aarav takes 72 seconds and Kabir 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?
  23. 23.Aarav 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?
  24. 24.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Ananya takes 48 seconds and Nisha 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?
  26. 26.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 5 or 3.
  27. 27.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?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 5.
  29. 29.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 4.
  30. 30.Two tanks hold 90 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Manav takes 75 seconds and Isha 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?
  33. 33.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 4.
  34. 34.Three temple bells ring every 6, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 15 litres and 35 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 8, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 175 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Three temple bells ring every 24, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 20, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 183
  2. 10
  3. 60
  4. 270
  5. 180
  6. 120
  7. 32
  8. 60
  9. 15
  10. 720
  11. 90
  12. 10
  13. 120
  14. 5
  15. 30
  16. 6
  17. 20
  18. 40
  19. 183
  20. 216
  21. 120
  22. 360
  23. 400
  24. 10
  25. 240
  26. 46
  27. 24
  28. 17
  29. 37
  30. 45
  31. 10
  32. 150
  33. 26
  34. 72
  35. 5
  36. 120
  37. 25
  38. 72
  39. 42
  40. 40

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