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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 458 · 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.Ishaan takes 45 seconds and Farhan 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?
  2. 2.Two tanks hold 90 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Saanvi takes 45 seconds and Sneha 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?
  4. 4.Nisha takes 80 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.Three temple bells ring every 4, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 4.
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 10 or 4.
  8. 8.Two tanks hold 30 litres and 135 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 9 that leaves a remainder of 2 when divided by 9, 8 or 3.
  10. 10.Two tanks hold 15 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Three temple bells ring every 4, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 9, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Kavya takes 60 seconds and Vivaan 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?
  14. 14.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 8, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 8 or 4.
  17. 17.Find the smallest number bigger than 9 that leaves a remainder of 4 when divided by 9, 6 or 5.
  18. 18.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?
  19. 19.Arjun takes 40 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?
  20. 20.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?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 10 or 3.
  22. 22.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Manav takes 72 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?
  24. 24.Priya takes 36 seconds and Meera 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?
  25. 25.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 3 or 12.
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 6 or 15.
  27. 27.Two tanks hold 320 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Two tanks hold 80 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Three temple bells ring every 15, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 8, 10 or 4.
  31. 31.Three temple bells ring every 9, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 210 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Ananya takes 75 seconds and Tara 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?
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 6 or 10.
  35. 35.Two tanks hold 160 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Two tanks hold 140 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  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.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 4 or 3.
  39. 39.Two tanks hold 80 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Two tanks hold 225 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 360
  2. 30
  3. 180
  4. 400
  5. 60
  6. 37
  7. 63
  8. 15
  9. 74
  10. 5
  11. 72
  12. 36
  13. 180
  14. 40
  15. 72
  16. 75
  17. 94
  18. 56
  19. 360
  20. 40
  21. 121
  22. 10
  23. 360
  24. 720
  25. 13
  26. 61
  27. 40
  28. 20
  29. 60
  30. 43
  31. 36
  32. 30
  33. 150
  34. 62
  35. 40
  36. 20
  37. 20
  38. 61
  39. 20
  40. 45

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