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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 233 · 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.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?
  2. 2.Two tanks hold 40 litres and 100 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 140 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Ananya takes 54 seconds and Tara 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?
  5. 5.Nisha takes 36 seconds and Sneha 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.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Meera takes 30 seconds and Karan 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?
  8. 8.Two tanks hold 80 litres and 120 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 15 that leaves a remainder of 3 when divided by 6, 15 or 4.
  10. 10.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 4 or 9.
  11. 11.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 10.
  12. 12.Nisha takes 72 seconds and Diya 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?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 5 or 15.
  14. 14.Pooja takes 30 seconds and Aditya 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?
  15. 15.Three temple bells ring every 30, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 24, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Diya takes 50 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?
  18. 18.Two tanks hold 90 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Three temple bells ring every 24, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 6 or 10.
  22. 22.Three temple bells ring every 6, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 20, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Rohan takes 45 seconds and Arjun 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?
  25. 25.Three temple bells ring every 24, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 24, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 9 or 10.
  28. 28.Sneha 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?
  29. 29.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 6, 10 or 8.
  30. 30.Three temple bells ring every 5, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 5 or 8.
  32. 32.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 8 or 4.
  33. 33.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?
  34. 34.Aditya takes 45 seconds and Rohan 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?
  35. 35.Two tanks hold 405 litres and 180 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 75 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.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?
  38. 38.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Aarav takes 45 seconds and Kabir 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?
  40. 40.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?

Answer key

  1. 15
  2. 20
  3. 20
  4. 216
  5. 180
  6. 20
  7. 120
  8. 40
  9. 63
  10. 37
  11. 62
  12. 216
  13. 63
  14. 150
  15. 60
  16. 120
  17. 200
  18. 30
  19. 42
  20. 120
  21. 63
  22. 90
  23. 60
  24. 360
  25. 120
  26. 72
  27. 91
  28. 144
  29. 124
  30. 120
  31. 123
  32. 42
  33. 45
  34. 360
  35. 45
  36. 15
  37. 56
  38. 10
  39. 180
  40. 24

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