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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 452 · 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 15 that leaves a remainder of 1 when divided by 15, 3 or 4.
  2. 2.Two tanks hold 60 litres and 70 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, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Three temple bells ring every 6, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Three temple bells ring every 30, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Vivaan takes 30 seconds and Zoya 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?
  9. 9.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?
  10. 10.Three temple bells ring every 9, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 9, 10 or 15.
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 3.
  14. 14.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 8 or 9.
  15. 15.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Three temple bells ring every 9, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 9 or 12.
  18. 18.Three temple bells ring every 4, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 8, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 5, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Kabir takes 48 seconds and Sneha 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?
  22. 22.Arjun takes 45 seconds and Farhan 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?
  23. 23.Three temple bells ring every 4, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Two tanks hold 225 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.A hall floor is 120 cm long and 100 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 12 that leaves a remainder of 2 when divided by 12, 3 or 9.
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 5 or 9.
  29. 29.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?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 8 or 4.
  31. 31.Two tanks hold 405 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Two tanks hold 175 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 12, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 120 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Arjun takes 48 seconds and Nisha 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?
  36. 36.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?
  37. 37.Three temple bells ring every 6, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Two tanks hold 400 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Rohan takes 36 seconds and Ananya 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?
  40. 40.Two tanks hold 105 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 61
  2. 10
  3. 60
  4. 21
  5. 60
  6. 42
  7. 60
  8. 150
  9. 15
  10. 72
  11. 10
  12. 93
  13. 31
  14. 74
  15. 12
  16. 90
  17. 182
  18. 24
  19. 120
  20. 30
  21. 432
  22. 360
  23. 40
  24. 20
  25. 45
  26. 30
  27. 38
  28. 184
  29. 35
  30. 121
  31. 45
  32. 25
  33. 120
  34. 20
  35. 240
  36. 6
  37. 36
  38. 50
  39. 720
  40. 15

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