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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 488 · 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.Aarav takes 60 seconds and Kabir 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?
  2. 2.Three temple bells ring every 5, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 30, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 140 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Three temple bells ring every 4, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Kavya takes 30 seconds and Vivaan 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?
  7. 7.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 8.
  8. 8.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Three temple bells ring every 24, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 5, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Two tanks hold 100 litres and 60 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 20, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Kavya takes 45 seconds and Tara 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?
  15. 15.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 5.
  16. 16.A hall floor is 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Two tanks hold 120 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.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?
  20. 20.Two tanks hold 450 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 6, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Nisha takes 80 seconds and Zoya 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.A hall floor is 420 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Three temple bells ring every 8, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 15, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 6, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 30, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 360 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Two tanks hold 100 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Aditya takes 54 seconds and Meera 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?
  31. 31.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 3 or 9.
  32. 32.Two tanks hold 30 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 18, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 3, 4 or 5.
  35. 35.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 6 or 5.
  36. 36.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Two tanks hold 400 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.A hall floor is 60 cm long and 40 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 12, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 300
  2. 20
  3. 120
  4. 20
  5. 120
  6. 90
  7. 73
  8. 6
  9. 72
  10. 60
  11. 56
  12. 20
  13. 60
  14. 360
  15. 31
  16. 40
  17. 15
  18. 35
  19. 50
  20. 50
  21. 72
  22. 720
  23. 28
  24. 120
  25. 60
  26. 60
  27. 90
  28. 40
  29. 20
  30. 540
  31. 38
  32. 5
  33. 72
  34. 61
  35. 31
  36. 6
  37. 50
  38. 10
  39. 6
  40. 60

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