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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 20 · 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 10, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Zoya takes 48 seconds and Farhan 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?
  3. 3.Two tanks hold 180 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.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?
  5. 5.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Ishaan takes 40 seconds and Aarav 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?
  7. 7.Vivaan takes 45 seconds and Farhan takes 30 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.Nisha takes 50 seconds and Aarav 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?
  9. 9.Two tanks hold 160 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.Three temple bells ring every 5, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 105 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Kavya takes 90 seconds and Karan 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?
  14. 14.Two tanks hold 405 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.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?
  16. 16.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 3, 4 or 5.
  17. 17.Three temple bells ring every 8, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 8.
  19. 19.Ananya takes 72 seconds and Rahul takes 30 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.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 6.
  21. 21.Three temple bells ring every 24, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 10, 6 and 15 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 4 when divided by 15, 12 or 6.
  24. 24.Two tanks hold 100 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Karan takes 75 seconds and Saanvi 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?
  26. 26.Nisha takes 72 seconds and Priya 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?
  27. 27.Two tanks hold 35 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 24, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 15, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 9, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 180 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Two tanks hold 80 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 6, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.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?
  35. 35.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?
  36. 36.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 5 or 15.
  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.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 4, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 120
  2. 720
  3. 30
  4. 14
  5. 14
  6. 360
  7. 90
  8. 400
  9. 20
  10. 60
  11. 15
  12. 35
  13. 360
  14. 45
  15. 6
  16. 61
  17. 72
  18. 121
  19. 360
  20. 37
  21. 120
  22. 30
  23. 64
  24. 50
  25. 300
  26. 360
  27. 5
  28. 120
  29. 60
  30. 90
  31. 45
  32. 20
  33. 90
  34. 20
  35. 20
  36. 6
  37. 46
  38. 10
  39. 40
  40. 72

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