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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 174 · 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.Saanvi takes 50 seconds and Pooja 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?
  2. 2.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 5 or 12.
  4. 4.Three temple bells ring every 9, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 8, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Aarav takes 72 seconds and Kabir 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?
  8. 8.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?
  9. 9.Two tanks hold 30 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Two tanks hold 135 litres and 90 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 45 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 8.
  13. 13.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 12 or 5.
  15. 15.Kavya 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?
  16. 16.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?
  17. 17.Two tanks hold 200 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Two tanks hold 270 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Three temple bells ring every 4, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.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?
  22. 22.Karan takes 60 seconds and Zoya 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?
  23. 23.Nisha takes 72 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?
  24. 24.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 4 or 3.
  25. 25.Karan takes 30 seconds and Diya 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?
  26. 26.Three temple bells ring every 20, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 30 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 4.
  29. 29.Three temple bells ring every 4, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 6, 9 or 12.
  31. 31.Three temple bells ring every 12, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Saanvi takes 50 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?
  33. 33.Two tanks hold 45 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Diya takes 90 seconds and Isha 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?
  35. 35.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?
  36. 36.Three temple bells ring every 20, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 3 or 10.
  38. 38.A hall floor is 200 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Two tanks hold 60 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 150
  2. 42
  3. 61
  4. 72
  5. 120
  6. 15
  7. 360
  8. 15
  9. 5
  10. 45
  11. 5
  12. 25
  13. 21
  14. 61
  15. 216
  16. 45
  17. 40
  18. 30
  19. 60
  20. 12
  21. 56
  22. 240
  23. 360
  24. 13
  25. 180
  26. 60
  27. 10
  28. 14
  29. 24
  30. 39
  31. 60
  32. 200
  33. 5
  34. 270
  35. 35
  36. 60
  37. 31
  38. 40
  39. 30
  40. 15

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