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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 381 · 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 9 that leaves a remainder of 2 when divided by 8, 9 or 4.
  2. 2.Saanvi takes 60 seconds and Dev 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.Find the smallest number bigger than 8 that leaves a remainder of 4 when divided by 6, 5 or 8.
  4. 4.Two tanks hold 60 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.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?
  6. 6.Three temple bells ring every 15, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 3.
  8. 8.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Three temple bells ring every 4, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Manav takes 90 seconds and Vivaan 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?
  11. 11.Two tanks hold 45 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Three temple bells ring every 5, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Ishaan takes 36 seconds and Kabir 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.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 3 or 10.
  15. 15.Three temple bells ring every 12, 20 and 5 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 10 that leaves a remainder of 3 when divided by 4, 6 or 10.
  17. 17.Two tanks hold 20 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 8 or 10.
  19. 19.Two tanks hold 200 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Three temple bells ring every 6, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.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?
  22. 22.Three temple bells ring every 10, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 5 or 15.
  24. 24.Three temple bells ring every 30, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Karan takes 72 seconds and Tara 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?
  26. 26.Two tanks hold 200 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Two tanks hold 75 litres and 30 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, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Manav takes 48 seconds and Sneha 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?
  31. 31.Three temple bells ring every 4, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 10 or 15.
  33. 33.Pooja takes 60 seconds and Karan 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 15 that leaves a remainder of 4 when divided by 12, 15 or 8.
  35. 35.Three temple bells ring every 6, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Ishaan takes 40 seconds and Zoya 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?
  38. 38.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Rahul takes 45 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?
  40. 40.Three temple bells ring every 6, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 74
  2. 180
  3. 124
  4. 15
  5. 40
  6. 120
  7. 37
  8. 10
  9. 24
  10. 360
  11. 15
  12. 40
  13. 180
  14. 61
  15. 60
  16. 63
  17. 5
  18. 123
  19. 40
  20. 60
  21. 24
  22. 60
  23. 62
  24. 60
  25. 144
  26. 40
  27. 12
  28. 15
  29. 60
  30. 720
  31. 120
  32. 31
  33. 300
  34. 124
  35. 36
  36. 14
  37. 360
  38. 35
  39. 360
  40. 90

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