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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 42 · 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.Sneha takes 50 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?
  2. 2.Arjun takes 36 seconds and Dev 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?
  3. 3.Three temple bells ring every 15, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 25 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Find the smallest number bigger than 8 that leaves a remainder of 4 when divided by 5, 6 or 8.
  6. 6.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?
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 5 or 15.
  8. 8.Three temple bells ring every 4, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 30, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 60 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Three temple bells ring every 6, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.A hall floor is 360 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 30, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Two tanks hold 80 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Kavya takes 80 seconds and Farhan 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?
  19. 19.Ishaan 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?
  20. 20.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 8.
  21. 21.Two tanks hold 75 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 6 or 3.
  23. 23.Three temple bells ring every 8, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 20, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 10 or 8.
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 8 or 6.
  27. 27.Three temple bells ring every 15, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 240 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Three temple bells ring every 6, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Two tanks hold 50 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Two tanks hold 400 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.Two tanks hold 140 litres and 120 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 20, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Sneha takes 30 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?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 15 or 9.
  36. 36.Two tanks hold 125 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 10 or 6.
  38. 38.Three temple bells ring every 18, 24 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 12 that leaves a remainder of 2 when divided by 10, 12 or 4.
  40. 40.A hall floor is 300 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 400
  2. 360
  3. 120
  4. 5
  5. 124
  6. 40
  7. 62
  8. 36
  9. 120
  10. 30
  11. 50
  12. 90
  13. 40
  14. 24
  15. 120
  16. 12
  17. 10
  18. 400
  19. 216
  20. 25
  21. 15
  22. 20
  23. 120
  24. 120
  25. 121
  26. 25
  27. 60
  28. 30
  29. 90
  30. 10
  31. 50
  32. 20
  33. 40
  34. 120
  35. 49
  36. 25
  37. 31
  38. 72
  39. 62
  40. 30

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