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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 2 · 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 18, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 100 litres and 75 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 24, 8 and 30 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 10 that leaves a remainder of 5 when divided by 6, 10 or 9.
  5. 5.Three temple bells ring every 20, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 8, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 6 or 12.
  8. 8.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 10 or 15.
  10. 10.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 5.
  11. 11.Three temple bells ring every 15, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 6.
  13. 13.Three temple bells ring every 8, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Rahul takes 60 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?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 5.
  16. 16.Two tanks hold 45 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Rahul takes 72 seconds and Diya 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?
  18. 18.Kavya takes 30 seconds and Nisha takes 50 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.Three temple bells ring every 6, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 6, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Dev takes 75 seconds and Aditya 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.Saanvi takes 54 seconds and Ananya 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?
  23. 23.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 5 or 4.
  24. 24.Two tanks hold 30 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 6, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 20, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 8, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.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?
  30. 30.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Two tanks hold 160 litres and 200 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 25 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Two tanks hold 60 litres and 90 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 20 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 10.
  37. 37.Three temple bells ring every 5, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Karan takes 36 seconds and Pooja 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?
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 12 or 8.

Answer key

  1. 90
  2. 25
  3. 120
  4. 95
  5. 40
  6. 120
  7. 14
  8. 20
  9. 34
  10. 122
  11. 120
  12. 19
  13. 40
  14. 180
  15. 61
  16. 5
  17. 720
  18. 150
  19. 120
  20. 72
  21. 600
  22. 270
  23. 62
  24. 10
  25. 10
  26. 120
  27. 120
  28. 120
  29. 21
  30. 20
  31. 40
  32. 5
  33. 56
  34. 30
  35. 10
  36. 181
  37. 20
  38. 12
  39. 180
  40. 124

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