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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 12 · 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 6, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 9, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.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?
  4. 4.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 4 or 5.
  5. 5.Two tanks hold 350 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.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?
  7. 7.Three temple bells ring every 10, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 6 or 5.
  9. 9.Three temple bells ring every 8, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 405 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 6, 5 or 3.
  12. 12.Two tanks hold 140 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 4, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Two tanks hold 120 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Manav takes 72 seconds and Sneha 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?
  16. 16.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 4 or 15.
  17. 17.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?
  18. 18.Manav takes 30 seconds and Pooja 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?
  19. 19.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Three temple bells ring every 9, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 24, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Three temple bells ring every 15, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 3 or 5.
  26. 26.Two tanks hold 60 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Two tanks hold 60 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Aarav takes 72 seconds and Pooja 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.Three temple bells ring every 24, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 15, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 5, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 280 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 5.
  34. 34.Three temple bells ring every 6, 10 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Aarav takes 54 seconds and Kavya takes 60 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?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 5 or 8.
  38. 38.Two tanks hold 70 litres and 80 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 75 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 8 or 4.

Answer key

  1. 60
  2. 36
  3. 30
  4. 63
  5. 50
  6. 12
  7. 90
  8. 62
  9. 40
  10. 45
  11. 32
  12. 20
  13. 72
  14. 30
  15. 720
  16. 181
  17. 24
  18. 120
  19. 15
  20. 90
  21. 120
  22. 12
  23. 56
  24. 120
  25. 31
  26. 20
  27. 30
  28. 360
  29. 120
  30. 60
  31. 90
  32. 40
  33. 122
  34. 90
  35. 40
  36. 540
  37. 124
  38. 10
  39. 25
  40. 73

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