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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 532 · 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.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 4.
  2. 2.Diya takes 75 seconds and Aarav 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?
  3. 3.Three temple bells ring every 30, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 120 litres and 105 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 120 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Find the smallest number bigger than 8 that leaves a remainder of 4 when divided by 6, 8 or 5.
  7. 7.Three temple bells ring every 6, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 75 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Two tanks hold 15 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.Three temple bells ring every 10, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 200 litres and 120 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 10 that leaves a remainder of 2 when divided by 6, 10 or 9.
  13. 13.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?
  14. 14.Three temple bells ring every 24, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 4 or 5.
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 10 or 6.
  17. 17.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?
  18. 18.Two tanks hold 45 litres and 25 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 18, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 12, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Two tanks hold 10 litres and 45 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 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Aarav takes 30 seconds and Nisha 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.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 15 or 3.
  25. 25.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?
  26. 26.Two tanks hold 10 litres and 35 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 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Two tanks hold 150 litres and 90 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 6, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.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?
  32. 32.Ishaan takes 54 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?
  33. 33.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?
  34. 34.Nisha takes 48 seconds and Dev takes 80 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.Three temple bells ring every 9, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.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?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 6, 12 or 8.
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 12, 8 or 15.
  39. 39.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 10 or 9.
  40. 40.Three temple bells ring every 5, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 37
  2. 150
  3. 120
  4. 15
  5. 15
  6. 124
  7. 90
  8. 15
  9. 5
  10. 120
  11. 40
  12. 92
  13. 35
  14. 120
  15. 41
  16. 63
  17. 50
  18. 5
  19. 90
  20. 60
  21. 5
  22. 56
  23. 90
  24. 62
  25. 10
  26. 5
  27. 30
  28. 30
  29. 72
  30. 20
  31. 14
  32. 432
  33. 21
  34. 240
  35. 72
  36. 28
  37. 27
  38. 126
  39. 92
  40. 60

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