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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 191 · 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 2 when divided by 12, 6 or 3.
  2. 2.Two tanks hold 120 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.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?
  4. 4.Meera takes 60 seconds and Pooja 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?
  5. 5.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 3 or 15.
  7. 7.Rohan takes 40 seconds and Ananya takes 75 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.Two tanks hold 320 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 5.
  10. 10.Three temple bells ring every 30, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 10 or 15.
  12. 12.Three temple bells ring every 5, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 6, 10 or 5.
  14. 14.Priya takes 40 seconds and Tara 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?
  15. 15.Three temple bells ring every 10, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 20, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 6, 3 or 8.
  18. 18.Three temple bells ring every 4, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Tara takes 36 seconds and Priya 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?
  20. 20.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?
  21. 21.Two tanks hold 105 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Two tanks hold 50 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Ananya takes 75 seconds and Saanvi 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?
  24. 24.Three temple bells ring every 18, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 8, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 180 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 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Farhan takes 72 seconds and Aarav 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?
  29. 29.Three temple bells ring every 8, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 6, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 360 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.Three temple bells ring every 20, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Three temple bells ring every 18, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 120 litres and 90 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 15 that leaves a remainder of 6 when divided by 10, 12 or 15.
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 8, 5 or 10.
  38. 38.Two tanks hold 75 litres and 50 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 80 litres and 30 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 12 that leaves a remainder of 2 when divided by 9, 12 or 3.

Answer key

  1. 14
  2. 15
  3. 25
  4. 300
  5. 28
  6. 32
  7. 600
  8. 40
  9. 121
  10. 120
  11. 31
  12. 60
  13. 34
  14. 120
  15. 40
  16. 60
  17. 26
  18. 20
  19. 360
  20. 40
  21. 15
  22. 25
  23. 300
  24. 90
  25. 120
  26. 20
  27. 45
  28. 144
  29. 72
  30. 60
  31. 40
  32. 120
  33. 15
  34. 72
  35. 30
  36. 66
  37. 42
  38. 25
  39. 10
  40. 38

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