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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 357 · 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 8 that leaves a remainder of 2 when divided by 5, 8 or 4.
  2. 2.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Two tanks hold 175 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Arjun takes 50 seconds and Kavya 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?
  5. 5.Manav takes 90 seconds and Kavya 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?
  6. 6.Aarav takes 72 seconds and Diya 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?
  7. 7.Three temple bells ring every 8, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 90 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Two tanks hold 135 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Three temple bells ring every 9, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Two tanks hold 315 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 6 or 9.
  15. 15.Two tanks hold 100 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Ananya takes 36 seconds and Tara 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?
  17. 17.A hall floor is 180 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Three temple bells ring every 8, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 100 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Two tanks hold 210 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Two tanks hold 80 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.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?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 4.
  25. 25.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?
  26. 26.Two tanks hold 250 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 18, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.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?
  29. 29.Three temple bells ring every 15, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Diya takes 30 seconds and Meera 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?
  31. 31.Farhan takes 50 seconds and Sneha 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?
  32. 32.Farhan takes 45 seconds and Zoya 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?
  33. 33.Arjun takes 36 seconds and Kavya 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?
  34. 34.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 15 or 5.
  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.Isha takes 75 seconds and Nisha 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?
  37. 37.Three temple bells ring every 18, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 180 cm long and 120 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 6, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 6 or 15.

Answer key

  1. 42
  2. 25
  3. 25
  4. 450
  5. 180
  6. 216
  7. 72
  8. 10
  9. 24
  10. 15
  11. 90
  12. 10
  13. 45
  14. 20
  15. 20
  16. 180
  17. 30
  18. 40
  19. 20
  20. 6
  21. 30
  22. 40
  23. 56
  24. 63
  25. 72
  26. 50
  27. 72
  28. 56
  29. 30
  30. 180
  31. 400
  32. 270
  33. 108
  34. 63
  35. 60
  36. 150
  37. 36
  38. 6
  39. 60
  40. 31

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