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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 139 · 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.Aarav takes 72 seconds and Priya 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?
  2. 2.Three temple bells ring every 18, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 8.
  4. 4.Three temple bells ring every 18, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Kavya takes 48 seconds and Ishaan 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 45 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.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?
  8. 8.Three temple bells ring every 24, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 12, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.A hall floor is 200 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.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?
  12. 12.Two tanks hold 315 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 12, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Meera takes 30 seconds and Diya 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?
  15. 15.Two tanks hold 250 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 4 or 10.
  17. 17.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Three temple bells ring every 12, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.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?
  20. 20.Karan takes 75 seconds and Ananya 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?
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 15, 9 or 12.
  22. 22.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?
  23. 23.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 8 or 3.
  24. 24.Two tanks hold 15 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 30, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Nisha takes 90 seconds and Diya 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?
  27. 27.Two tanks hold 405 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 9.
  29. 29.Three temple bells ring every 15, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Three temple bells ring every 6, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 12 or 6.
  35. 35.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 5 or 10.
  36. 36.Two tanks hold 30 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.Two tanks hold 315 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Two tanks hold 120 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 4 or 12.
  40. 40.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 720
  2. 90
  3. 122
  4. 90
  5. 144
  6. 5
  7. 120
  8. 120
  9. 120
  10. 40
  11. 20
  12. 45
  13. 60
  14. 120
  15. 50
  16. 61
  17. 42
  18. 120
  19. 20
  20. 300
  21. 187
  22. 42
  23. 73
  24. 5
  25. 60
  26. 450
  27. 45
  28. 46
  29. 60
  30. 12
  31. 56
  32. 120
  33. 56
  34. 61
  35. 91
  36. 10
  37. 45
  38. 30
  39. 63
  40. 21

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