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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 123 · 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.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?
  3. 3.Two tanks hold 135 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Aditya takes 50 seconds and Dev 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?
  5. 5.Two tanks hold 180 litres and 160 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, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 200 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Manav takes 40 seconds and Nisha 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?
  9. 9.Two tanks hold 225 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Two tanks hold 160 litres and 60 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 10, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 10, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Two tanks hold 400 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Kabir takes 30 seconds and Meera 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?
  15. 15.Ananya takes 54 seconds and Arjun 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?
  16. 16.Two tanks hold 100 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Two tanks hold 30 litres and 20 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 6, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Ishaan takes 30 seconds and Sneha 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?
  21. 21.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 9 or 6.
  22. 22.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?
  23. 23.Three temple bells ring every 9, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 3, 5 or 4.
  26. 26.Three temple bells ring every 8, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 12 or 5.
  29. 29.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?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 3 or 15.
  31. 31.Kavya takes 36 seconds and Isha 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?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 8 or 15.
  33. 33.Pooja takes 40 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.Sneha takes 75 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?
  35. 35.Three temple bells ring every 10, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 24, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Diya takes 48 seconds and Farhan 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?
  38. 38.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?
  39. 39.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 4 or 10.

Answer key

  1. 13
  2. 35
  3. 15
  4. 200
  5. 20
  6. 30
  7. 25
  8. 600
  9. 45
  10. 20
  11. 60
  12. 60
  13. 50
  14. 240
  15. 432
  16. 20
  17. 30
  18. 10
  19. 60
  20. 90
  21. 91
  22. 21
  23. 72
  24. 6
  25. 61
  26. 72
  27. 42
  28. 63
  29. 56
  30. 61
  31. 180
  32. 122
  33. 200
  34. 300
  35. 60
  36. 120
  37. 144
  38. 45
  39. 6
  40. 62

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