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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 151 · 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.Rahul takes 40 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?
  2. 2.Two tanks hold 30 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.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?
  4. 4.Two tanks hold 225 litres and 175 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 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 4.
  7. 7.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 5 or 6.
  8. 8.Two tanks hold 90 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Three temple bells ring every 6, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Sneha takes 72 seconds and Pooja 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?
  11. 11.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  12. 12.Two tanks hold 225 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 5 or 3.
  14. 14.Dev takes 40 seconds and Kabir takes 75 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 35 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Two tanks hold 15 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 12, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.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?
  19. 19.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.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?
  21. 21.Two tanks hold 200 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Three temple bells ring every 5, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Ananya takes 72 seconds and Aarav 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?
  25. 25.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 4 or 6.
  26. 26.Two tanks hold 320 litres and 120 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 12, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 270 litres and 240 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 10, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Two tanks hold 360 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 12 or 4.
  32. 32.Rohan takes 30 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?
  33. 33.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 3 or 6.
  34. 34.Three temple bells ring every 15, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 30, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 5, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Manav takes 45 seconds and Nisha 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?
  38. 38.Vivaan takes 75 seconds and Diya 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?
  39. 39.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 200
  2. 15
  3. 35
  4. 25
  5. 40
  6. 61
  7. 121
  8. 30
  9. 60
  10. 360
  11. 31
  12. 45
  13. 32
  14. 600
  15. 5
  16. 5
  17. 60
  18. 12
  19. 35
  20. 24
  21. 50
  22. 10
  23. 60
  24. 360
  25. 63
  26. 40
  27. 120
  28. 30
  29. 60
  30. 40
  31. 62
  32. 90
  33. 13
  34. 60
  35. 120
  36. 40
  37. 270
  38. 600
  39. 21
  40. 56

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