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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 509 · 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.Diya takes 54 seconds and Arjun 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?
  2. 2.Tara takes 48 seconds and Nisha 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?
  3. 3.Two tanks hold 140 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Two tanks hold 150 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Meera takes 50 seconds and Vivaan 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?
  7. 7.Isha takes 72 seconds and Saanvi 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?
  8. 8.Three temple bells ring every 18, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 24, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 8 or 6.
  11. 11.Three temple bells ring every 5, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 12 or 10.
  14. 14.Kavya takes 60 seconds and Isha 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?
  15. 15.Two tanks hold 100 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 10.
  17. 17.Three temple bells ring every 4, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 4, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 6, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 30, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Three temple bells ring every 5, 30 and 12 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 12 that leaves a remainder of 1 when divided by 5, 8 or 12.
  24. 24.Three temple bells ring every 12, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.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?
  26. 26.Two tanks hold 210 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Ishaan takes 50 seconds and Tara 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?
  28. 28.Three temple bells ring every 24, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 225 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 30, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 150 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 8, 3 or 10.
  34. 34.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 5, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Three temple bells ring every 8, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Three temple bells ring every 20, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Tara takes 30 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?

Answer key

  1. 540
  2. 720
  3. 20
  4. 50
  5. 56
  6. 300
  7. 360
  8. 90
  9. 120
  10. 125
  11. 60
  12. 40
  13. 121
  14. 540
  15. 50
  16. 62
  17. 60
  18. 60
  19. 24
  20. 90
  21. 28
  22. 60
  23. 121
  24. 60
  25. 35
  26. 30
  27. 450
  28. 120
  29. 45
  30. 60
  31. 50
  32. 12
  33. 122
  34. 24
  35. 60
  36. 12
  37. 120
  38. 35
  39. 120
  40. 150

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