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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 554 · 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.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 3.
  2. 2.Two tanks hold 45 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.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?
  4. 4.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?
  5. 5.Aarav takes 72 seconds and Arjun 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?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 4 or 10.
  7. 7.Three temple bells ring every 10, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 20, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 12 or 15.
  11. 11.A hall floor is 315 cm long and 90 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 1 when divided by 12, 9 or 3.
  13. 13.Two tanks hold 80 litres and 200 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 150 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 9 or 8.
  17. 17.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Two tanks hold 100 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Three temple bells ring every 24, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 24, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  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.Three temple bells ring every 20, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 8 or 9.
  25. 25.Three temple bells ring every 6, 18 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 6 or 4.
  27. 27.Diya takes 40 seconds and Priya 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?
  28. 28.A hall floor is 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Two tanks hold 120 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Two tanks hold 90 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 18, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 4, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Rahul takes 90 seconds and Priya 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?
  34. 34.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 10, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 9, 30 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Aarav takes 48 seconds and Saanvi 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?
  38. 38.Saanvi takes 30 seconds and Rahul 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?
  39. 39.Two tanks hold 210 litres and 60 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 3, 4 or 9.

Answer key

  1. 13
  2. 5
  3. 35
  4. 6
  5. 360
  6. 62
  7. 120
  8. 60
  9. 24
  10. 64
  11. 14
  12. 37
  13. 40
  14. 25
  15. 12
  16. 73
  17. 21
  18. 25
  19. 120
  20. 120
  21. 15
  22. 12
  23. 60
  24. 73
  25. 90
  26. 26
  27. 360
  28. 56
  29. 40
  30. 15
  31. 90
  32. 60
  33. 720
  34. 14
  35. 60
  36. 90
  37. 144
  38. 270
  39. 30
  40. 37

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