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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 451 · 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.Kabir takes 36 seconds and Manav 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?
  2. 2.Three temple bells ring every 8, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Two tanks hold 50 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Three temple bells ring every 20, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 6 or 4.
  6. 6.Manav takes 30 seconds and Pooja 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?
  7. 7.Three temple bells ring every 18, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 20, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 4, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Meera takes 60 seconds and Aarav 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?
  11. 11.A hall floor is 180 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Two tanks hold 280 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 6.
  14. 14.Three temple bells ring every 5, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 8, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Aditya 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?
  17. 17.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?
  18. 18.Three temple bells ring every 12, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.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?
  21. 21.Three temple bells ring every 5, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 8.
  23. 23.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 8, 9 or 3.
  24. 24.Nisha takes 72 seconds and Isha 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?
  25. 25.Three temple bells ring every 24, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.A hall floor is 225 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Three temple bells ring every 30, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.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?
  29. 29.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 8 or 4.
  30. 30.Two tanks hold 180 litres and 100 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 15, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 5, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 100 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.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?
  35. 35.Three temple bells ring every 9, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 12, 30 and 15 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 9 that leaves a remainder of 3 when divided by 4, 6 or 9.
  38. 38.A hall floor is 480 cm long and 180 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 30, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 9, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 108
  2. 120
  3. 10
  4. 60
  5. 61
  6. 180
  7. 36
  8. 120
  9. 60
  10. 240
  11. 30
  12. 40
  13. 14
  14. 120
  15. 120
  16. 432
  17. 56
  18. 60
  19. 42
  20. 56
  21. 120
  22. 122
  23. 74
  24. 360
  25. 120
  26. 15
  27. 60
  28. 21
  29. 75
  30. 20
  31. 45
  32. 20
  33. 20
  34. 15
  35. 90
  36. 60
  37. 39
  38. 24
  39. 120
  40. 72

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