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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 170 · 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, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Nisha takes 54 seconds and Rahul 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?
  3. 3.Three temple bells ring every 5, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Three temple bells ring every 20, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 15 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Aditya takes 40 seconds and Manav 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?
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 8 or 15.
  11. 11.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 6, 12 or 9.
  13. 13.Two tanks hold 90 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Two tanks hold 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.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?
  16. 16.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.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?
  18. 18.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?
  19. 19.Saanvi takes 30 seconds and Nisha takes 48 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?
  20. 20.Priya takes 40 seconds and Ananya 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.Three temple bells ring every 5, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Pooja takes 30 seconds and Rahul 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 10 that leaves a remainder of 2 when divided by 6, 3 or 10.
  24. 24.Two tanks hold 450 litres and 200 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 140 cm long and 100 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 18, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 8, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 80 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.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?
  30. 30.Pooja takes 54 seconds and Rahul 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?
  31. 31.Two tanks hold 270 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 9 or 8.
  34. 34.Three temple bells ring every 30, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 9.
  37. 37.Three temple bells ring every 6, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 6.
  39. 39.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 9, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 72
  2. 108
  3. 60
  4. 42
  5. 28
  6. 120
  7. 5
  8. 6
  9. 360
  10. 123
  11. 28
  12. 40
  13. 10
  14. 20
  15. 20
  16. 50
  17. 15
  18. 90
  19. 240
  20. 120
  21. 30
  22. 90
  23. 32
  24. 50
  25. 35
  26. 72
  27. 120
  28. 40
  29. 45
  30. 270
  31. 30
  32. 15
  33. 75
  34. 60
  35. 12
  36. 91
  37. 30
  38. 32
  39. 10
  40. 72

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