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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 216 · 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 10 that leaves a remainder of 1 when divided by 8, 3 or 10.
  2. 2.Rahul takes 60 seconds and Pooja 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?
  3. 3.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Meera takes 40 seconds and Zoya 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?
  5. 5.Zoya takes 40 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?
  6. 6.Three temple bells ring every 5, 30 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.A hall floor is 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Ananya takes 90 seconds and Priya 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?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 5 or 15.
  10. 10.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Manav takes 48 seconds and Dev 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?
  12. 12.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.A hall floor is 175 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Rahul takes 36 seconds and Priya 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?
  16. 16.Two tanks hold 60 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 5.
  18. 18.Diya takes 45 seconds and Arjun 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?
  19. 19.A hall floor is 210 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Three temple bells ring every 10, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 10, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 10 or 4.
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 3 or 15.
  24. 24.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?
  25. 25.Two tanks hold 350 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Pooja takes 30 seconds and Priya 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?
  27. 27.Saanvi takes 50 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?
  28. 28.Three temple bells ring every 12, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Nisha takes 40 seconds and Vivaan 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?
  30. 30.Three temple bells ring every 6, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 4, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 4, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 8, 12 or 6.
  34. 34.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 5, 3 or 4.
  35. 35.Priya takes 60 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?
  36. 36.Three temple bells ring every 30, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Arjun takes 54 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?
  38. 38.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?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 12 or 5.
  40. 40.Pooja takes 75 seconds and Dev 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?

Answer key

  1. 121
  2. 300
  3. 20
  4. 360
  5. 360
  6. 90
  7. 30
  8. 180
  9. 31
  10. 40
  11. 240
  12. 30
  13. 28
  14. 10
  15. 180
  16. 15
  17. 46
  18. 360
  19. 35
  20. 20
  21. 120
  22. 62
  23. 16
  24. 14
  25. 50
  26. 90
  27. 200
  28. 120
  29. 360
  30. 90
  31. 40
  32. 60
  33. 29
  34. 62
  35. 180
  36. 90
  37. 540
  38. 10
  39. 121
  40. 225

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