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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 152 · 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 5, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 4 or 15.
  5. 5.Sneha takes 80 seconds and Ishaan 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?
  6. 6.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 8 or 3.
  7. 7.Ananya takes 40 seconds and Aditya 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?
  8. 8.Three temple bells ring every 5, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 4.
  10. 10.Rohan takes 45 seconds and Zoya 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?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 9 or 4.
  12. 12.Two tanks hold 200 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 6 or 4.
  14. 14.Two tanks hold 210 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 8, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.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?
  17. 17.Tara takes 60 seconds and Manav 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?
  18. 18.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 5, 3 or 4.
  19. 19.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 3.
  20. 20.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?
  21. 21.Saanvi 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?
  22. 22.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 10, 9 or 15.
  24. 24.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?
  25. 25.Three temple bells ring every 8, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 30, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Three temple bells ring every 6, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Two tanks hold 45 litres and 60 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 30 litres and 105 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 400 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Two tanks hold 360 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Meera takes 36 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?
  35. 35.Three temple bells ring every 4, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.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?
  37. 37.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?
  38. 38.Three temple bells ring every 8, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 10, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.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?

Answer key

  1. 120
  2. 24
  3. 14
  4. 122
  5. 720
  6. 73
  7. 360
  8. 60
  9. 25
  10. 90
  11. 183
  12. 40
  13. 61
  14. 30
  15. 120
  16. 120
  17. 120
  18. 61
  19. 31
  20. 40
  21. 360
  22. 12
  23. 97
  24. 12
  25. 120
  26. 90
  27. 6
  28. 60
  29. 42
  30. 15
  31. 15
  32. 50
  33. 40
  34. 180
  35. 60
  36. 10
  37. 15
  38. 120
  39. 120
  40. 45

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