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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 70 · 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 4, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.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?
  3. 3.A hall floor is 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Three temple bells ring every 20, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 10, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 5, 6 or 3.
  7. 7.Find the smallest number bigger than 6 that leaves a remainder of 3 when divided by 4, 6 or 5.
  8. 8.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?
  9. 9.Three temple bells ring every 12, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 315 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 10 or 12.
  13. 13.Three temple bells ring every 30, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 5, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 18, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 90 litres and 80 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 12 that leaves a remainder of 2 when divided by 6, 12 or 9.
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 3 or 15.
  19. 19.Karan takes 40 seconds and Vivaan 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?
  20. 20.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Saanvi takes 45 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?
  22. 22.Meera takes 72 seconds and Zoya 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?
  23. 23.Three temple bells ring every 6, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 30, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 35 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Two tanks hold 150 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 15, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Three temple bells ring every 20, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Two tanks hold 70 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Zoya takes 60 seconds and Meera 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?
  32. 32.Three temple bells ring every 6, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 6, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 400 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 8 or 15.
  36. 36.Two tanks hold 120 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Farhan takes 48 seconds and Aditya 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?
  38. 38.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.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?
  40. 40.Three temple bells ring every 5, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 60
  2. 45
  3. 40
  4. 120
  5. 90
  6. 31
  7. 63
  8. 50
  9. 36
  10. 45
  11. 20
  12. 63
  13. 120
  14. 120
  15. 90
  16. 10
  17. 38
  18. 32
  19. 120
  20. 30
  21. 360
  22. 360
  23. 90
  24. 120
  25. 5
  26. 30
  27. 120
  28. 28
  29. 60
  30. 10
  31. 180
  32. 60
  33. 30
  34. 40
  35. 122
  36. 15
  37. 144
  38. 15
  39. 40
  40. 60

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