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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 10 · 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 12, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.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?
  3. 3.Three temple bells ring every 9, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 4 or 3.
  5. 5.Two tanks hold 360 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Three temple bells ring every 18, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Isha takes 45 seconds and Zoya 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?
  8. 8.Three temple bells ring every 6, 9 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 225 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.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?
  11. 11.Three temple bells ring every 24, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 24, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Manav takes 72 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?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 15, 10 or 9.
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 9 when divided by 10, 12 or 15.
  16. 16.Two tanks hold 75 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.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?
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 6 or 5.
  19. 19.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Two tanks hold 350 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.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?
  22. 22.Three temple bells ring every 4, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 160 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Aditya takes 75 seconds and Dev takes 90 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.Two tanks hold 10 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 10 or 8.
  27. 27.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Ananya takes 36 seconds and Aarav 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?
  29. 29.Find the smallest number bigger than 8 that leaves a remainder of 4 when divided by 6, 5 or 8.
  30. 30.Three temple bells ring every 15, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 6, 8 or 5.
  32. 32.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 6.
  33. 33.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Two tanks hold 80 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Two tanks hold 200 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Two tanks hold 140 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Diya takes 60 seconds and Kavya 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?
  38. 38.Three temple bells ring every 24, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Saanvi takes 50 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?
  40. 40.Three temple bells ring every 24, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 24
  2. 14
  3. 72
  4. 14
  5. 45
  6. 72
  7. 180
  8. 36
  9. 45
  10. 40
  11. 120
  12. 72
  13. 360
  14. 96
  15. 69
  16. 15
  17. 72
  18. 31
  19. 20
  20. 50
  21. 10
  22. 24
  23. 20
  24. 450
  25. 5
  26. 42
  27. 12
  28. 360
  29. 124
  30. 30
  31. 122
  32. 19
  33. 56
  34. 10
  35. 50
  36. 20
  37. 540
  38. 72
  39. 450
  40. 72

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