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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 257 · 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 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.Three temple bells ring every 6, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.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?
  5. 5.Isha takes 60 seconds and Tara 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?
  6. 6.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?
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 6 when divided by 8, 12 or 9.
  8. 8.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?
  9. 9.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 6 or 9.
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 5.
  11. 11.Meera takes 40 seconds and Dev 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?
  12. 12.Three temple bells ring every 10, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Two tanks hold 40 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 4, 6 or 8.
  15. 15.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?
  16. 16.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?
  17. 17.Karan takes 54 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?
  18. 18.Three temple bells ring every 15, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 12 or 4.
  20. 20.Three temple bells ring every 18, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.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?
  22. 22.Two tanks hold 150 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Two tanks hold 30 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 8 or 4.
  25. 25.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 9 or 10.
  26. 26.Three temple bells ring every 6, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 9 or 15.
  28. 28.Three temple bells ring every 18, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 8, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Kabir takes 40 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?
  31. 31.Two tanks hold 315 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 10.
  33. 33.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 5, 3 or 4.
  34. 34.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 12.
  35. 35.Two tanks hold 40 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Isha takes 80 seconds and Manav 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?
  37. 37.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?
  38. 38.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 5.
  39. 39.Ananya takes 40 seconds and Dev 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?
  40. 40.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?

Answer key

  1. 28
  2. 14
  3. 120
  4. 56
  5. 180
  6. 10
  7. 78
  8. 12
  9. 93
  10. 16
  11. 200
  12. 120
  13. 20
  14. 27
  15. 15
  16. 10
  17. 270
  18. 120
  19. 63
  20. 90
  21. 10
  22. 50
  23. 10
  24. 121
  25. 91
  26. 120
  27. 46
  28. 90
  29. 72
  30. 240
  31. 45
  32. 61
  33. 61
  34. 61
  35. 10
  36. 240
  37. 20
  38. 61
  39. 240
  40. 21

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