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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 190 · 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.Three temple bells ring every 10, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 8 or 3.
  4. 4.Ananya takes 30 seconds and Meera 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?
  5. 5.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 3 or 10.
  6. 6.Three temple bells ring every 15, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Diya takes 48 seconds and Kavya 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?
  8. 8.Three temple bells ring every 18, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Two tanks hold 40 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.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?
  12. 12.Three temple bells ring every 10, 30 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.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?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 6.
  15. 15.Three temple bells ring every 4, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Diya takes 40 seconds and Ishaan takes 72 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.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 5.
  18. 18.Two tanks hold 140 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Two tanks hold 50 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Ananya takes 45 seconds and Dev 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?
  21. 21.Aarav takes 30 seconds and Meera 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?
  22. 22.Two tanks hold 320 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Three temple bells ring every 24, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Tara takes 80 seconds and Arjun 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 8, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 8 or 12.
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 9 or 6.
  28. 28.Three temple bells ring every 4, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Arjun takes 36 seconds and Ananya 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?
  30. 30.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 4 or 6.
  31. 31.Three temple bells ring every 10, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.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?
  33. 33.Saanvi takes 30 seconds and Meera 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?
  34. 34.Two tanks hold 225 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 6.
  36. 36.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?
  37. 37.Three temple bells ring every 12, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Two tanks hold 30 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Two tanks hold 180 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Two tanks hold 60 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 90
  2. 21
  3. 122
  4. 90
  5. 31
  6. 120
  7. 240
  8. 90
  9. 40
  10. 5
  11. 56
  12. 90
  13. 21
  14. 31
  15. 60
  16. 360
  17. 46
  18. 20
  19. 10
  20. 90
  21. 120
  22. 40
  23. 120
  24. 720
  25. 120
  26. 122
  27. 95
  28. 120
  29. 108
  30. 39
  31. 120
  32. 14
  33. 270
  34. 45
  35. 14
  36. 35
  37. 60
  38. 10
  39. 45
  40. 15

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