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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 289 · 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).

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  1. 1.Two tanks hold 50 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Two tanks hold 210 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Pooja takes 72 seconds and Farhan 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?
  5. 5.A hall floor is 360 cm long and 315 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 12 that leaves a remainder of 3 when divided by 10, 6 or 12.
  7. 7.Two tanks hold 210 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Kavya takes 50 seconds and Arjun 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?
  9. 9.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 12 or 9.
  11. 11.Kavya takes 80 seconds and Manav 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?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 5 or 12.
  13. 13.Two tanks hold 105 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.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?
  15. 15.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?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 8 or 12.
  17. 17.Three temple bells ring every 4, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Ananya takes 40 seconds and Farhan 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.Three temple bells ring every 6, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Sneha takes 45 seconds and Vivaan 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?
  21. 21.Two tanks hold 100 litres and 225 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 20, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Two tanks hold 75 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 5 or 9.
  28. 28.Three temple bells ring every 8, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 4.
  31. 31.Saanvi takes 40 seconds and Aarav takes 30 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.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  33. 33.Tara takes 40 seconds and Saanvi 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?
  34. 34.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?
  35. 35.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?
  36. 36.Two tanks hold 75 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.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?
  38. 38.Three temple bells ring every 15, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Saanvi takes 50 seconds and Isha 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?
  40. 40.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 4 or 3.

Answer key

  1. 10
  2. 21
  3. 30
  4. 216
  5. 56
  6. 63
  7. 30
  8. 450
  9. 15
  10. 183
  11. 720
  12. 61
  13. 15
  14. 30
  15. 14
  16. 25
  17. 72
  18. 360
  19. 60
  20. 360
  21. 25
  22. 60
  23. 56
  24. 25
  25. 12
  26. 15
  27. 49
  28. 40
  29. 10
  30. 62
  31. 120
  32. 31
  33. 360
  34. 40
  35. 15
  36. 15
  37. 10
  38. 120
  39. 450
  40. 13

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