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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 321 · 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.Three temple bells ring every 8, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 5 or 3.
  3. 3.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?
  4. 4.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 5.
  5. 5.Vivaan takes 90 seconds and Kabir 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?
  6. 6.Two tanks hold 150 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Pooja takes 60 seconds and Nisha 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.Three temple bells ring every 9, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 5, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.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?
  11. 11.Two tanks hold 70 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 6 or 4.
  13. 13.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 3 or 12.
  15. 15.Isha takes 36 seconds and Arjun 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?
  16. 16.Two tanks hold 280 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 6 or 3.
  18. 18.Two tanks hold 50 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Meera takes 80 seconds and Dev 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.Rahul takes 54 seconds and Kavya 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.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Two tanks hold 60 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 5 or 12.
  25. 25.Arjun takes 75 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?
  26. 26.Three temple bells ring every 18, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 6, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 6, 12 or 3.
  29. 29.Ananya takes 50 seconds and Nisha 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?
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 10 or 3.
  31. 31.Two tanks hold 40 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 6 or 4.
  33. 33.Three temple bells ring every 8, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Meera takes 40 seconds and Rohan 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?
  35. 35.Three temple bells ring every 10, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Three temple bells ring every 10, 18 and 5 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 15 that leaves a remainder of 3 when divided by 10, 4 or 15.
  39. 39.Find the smallest number bigger than 9 that leaves a remainder of 4 when divided by 6, 8 or 9.
  40. 40.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 120
  2. 31
  3. 35
  4. 61
  5. 180
  6. 50
  7. 120
  8. 45
  9. 90
  10. 40
  11. 10
  12. 63
  13. 31
  14. 37
  15. 108
  16. 40
  17. 19
  18. 10
  19. 720
  20. 270
  21. 14
  22. 15
  23. 21
  24. 62
  25. 600
  26. 90
  27. 60
  28. 14
  29. 450
  30. 32
  31. 20
  32. 13
  33. 120
  34. 200
  35. 90
  36. 12
  37. 90
  38. 63
  39. 76
  40. 14

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