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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 50 · 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.Saanvi takes 30 seconds and Ananya 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?
  2. 2.Three temple bells ring every 24, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Isha takes 60 seconds and Zoya 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?
  4. 4.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Three temple bells ring every 24, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Dev takes 60 seconds and Meera 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?
  9. 9.Aarav takes 40 seconds and Nisha 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?
  10. 10.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Three temple bells ring every 8, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Two tanks hold 225 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Rohan takes 30 seconds and Dev 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?
  15. 15.Three temple bells ring every 10, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 105 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Meera takes 36 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?
  18. 18.Two tanks hold 40 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Ananya takes 45 seconds and Dev 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?
  20. 20.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 9 or 8.
  21. 21.Three temple bells ring every 8, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 18, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Ananya takes 40 seconds and Kavya 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?
  24. 24.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Two tanks hold 160 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Two tanks hold 150 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Two tanks hold 150 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 4 or 10.
  29. 29.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 6 or 15.
  30. 30.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?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 6 or 4.
  32. 32.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 4 or 6.
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 5 or 8.
  34. 34.Three temple bells ring every 4, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Dev takes 36 seconds and Aditya 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?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 12 or 10.
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 9 or 12.
  38. 38.Three temple bells ring every 5, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 8.
  40. 40.A hall floor is 300 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 180
  2. 120
  3. 120
  4. 14
  5. 56
  6. 42
  7. 120
  8. 300
  9. 120
  10. 35
  11. 28
  12. 40
  13. 25
  14. 240
  15. 90
  16. 15
  17. 180
  18. 10
  19. 360
  20. 75
  21. 72
  22. 90
  23. 200
  24. 42
  25. 40
  26. 30
  27. 30
  28. 61
  29. 62
  30. 20
  31. 62
  32. 14
  33. 124
  34. 60
  35. 108
  36. 62
  37. 37
  38. 60
  39. 122
  40. 20

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