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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 193 · 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 1 when divided by 3, 6 or 8.
  2. 2.Three temple bells ring every 5, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 9, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 4, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 6 or 5.
  6. 6.Two tanks hold 10 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Two tanks hold 70 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.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?
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 12 or 3.
  10. 10.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?
  11. 11.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Two tanks hold 60 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Two tanks hold 40 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Three temple bells ring every 9, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Isha takes 45 seconds and Aarav 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?
  16. 16.Two tanks hold 80 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Two tanks hold 125 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Rohan takes 80 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?
  19. 19.Two tanks hold 75 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Three temple bells ring every 6, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.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?
  22. 22.Three temple bells ring every 4, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 15, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 30, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 10, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 6 or 8.
  27. 27.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?
  28. 28.Two tanks hold 80 litres and 360 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 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Zoya takes 45 seconds and Sneha takes 48 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.Two tanks hold 15 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.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?
  33. 33.Two tanks hold 80 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 8.
  35. 35.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Three temple bells ring every 10, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Sneha takes 36 seconds and Kabir 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?
  39. 39.Two tanks hold 20 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Three temple bells ring every 8, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 25
  2. 90
  3. 90
  4. 36
  5. 34
  6. 5
  7. 10
  8. 28
  9. 37
  10. 40
  11. 6
  12. 10
  13. 10
  14. 45
  15. 360
  16. 20
  17. 25
  18. 720
  19. 15
  20. 60
  21. 30
  22. 24
  23. 120
  24. 60
  25. 60
  26. 123
  27. 6
  28. 40
  29. 50
  30. 720
  31. 5
  32. 60
  33. 40
  34. 26
  35. 14
  36. 60
  37. 15
  38. 180
  39. 10
  40. 120

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