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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 460 · 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.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Two tanks hold 90 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Three temple bells ring every 20, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 200 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Two tanks hold 80 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Manav takes 90 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?
  7. 7.Two tanks hold 105 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Two tanks hold 140 litres and 100 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 100 cm long and 80 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 8 that leaves a remainder of 1 when divided by 8, 5 or 6.
  11. 11.Find the smallest number bigger than 12 that leaves a remainder of 7 when divided by 12, 9 or 8.
  12. 12.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.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?
  14. 14.Isha takes 90 seconds and Aditya 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?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 9 when divided by 10, 12 or 15.
  16. 16.Rohan takes 50 seconds and Karan 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?
  17. 17.Three temple bells ring every 6, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.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?
  19. 19.A hall floor is 420 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Zoya takes 50 seconds and Manav 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?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 5 or 10.
  22. 22.Three temple bells ring every 15, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Pooja takes 75 seconds and Saanvi 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?
  24. 24.Three temple bells ring every 8, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Two tanks hold 140 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.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?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 5, 8 or 12.
  29. 29.A hall floor is 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.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?
  31. 31.Three temple bells ring every 30, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Ananya takes 30 seconds and Rahul 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?
  33. 33.Three temple bells ring every 30, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 6, 5 or 10.
  35. 35.Three temple bells ring every 12, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.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?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 10.
  38. 38.A hall floor is 200 cm long and 160 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 10, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.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?

Answer key

  1. 14
  2. 10
  3. 120
  4. 50
  5. 20
  6. 270
  7. 15
  8. 20
  9. 20
  10. 121
  11. 79
  12. 42
  13. 56
  14. 180
  15. 69
  16. 200
  17. 60
  18. 14
  19. 28
  20. 150
  21. 22
  22. 60
  23. 225
  24. 120
  25. 14
  26. 20
  27. 21
  28. 124
  29. 35
  30. 30
  31. 60
  32. 150
  33. 120
  34. 33
  35. 60
  36. 30
  37. 61
  38. 20
  39. 90
  40. 6

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