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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 337 · 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).

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  1. 1.Three temple bells ring every 4, 6 and 8 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 15 that leaves a remainder of 2 when divided by 15, 4 or 3.
  3. 3.Three temple bells ring every 9, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 5, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Two tanks hold 405 litres and 90 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 8, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.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?
  8. 8.Two tanks hold 90 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Nisha takes 72 seconds and Aarav 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?
  10. 10.Three temple bells ring every 15, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 25 litres and 15 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 15 that leaves a remainder of 2 when divided by 15, 12 or 10.
  13. 13.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Two tanks hold 210 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 8, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 9, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 12, 6 or 8.
  18. 18.Three temple bells ring every 15, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 8.
  20. 20.Manav takes 75 seconds and Nisha 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.Three temple bells ring every 9, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 4 or 10.
  23. 23.Three temple bells ring every 5, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Arjun takes 40 seconds and Saanvi 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?
  25. 25.Two tanks hold 175 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Farhan takes 36 seconds and Isha 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?
  27. 27.Pooja takes 60 seconds and Diya 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?
  28. 28.Two tanks hold 360 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.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?
  32. 32.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?
  33. 33.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Aditya takes 50 seconds and Kabir 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?
  35. 35.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 5 or 4.
  36. 36.Vivaan takes 50 seconds and Ananya 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?
  37. 37.Three temple bells ring every 4, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Karan takes 54 seconds and Kabir 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?
  39. 39.Manav takes 72 seconds and Diya 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?
  40. 40.Two tanks hold 100 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 24
  2. 62
  3. 90
  4. 120
  5. 45
  6. 120
  7. 56
  8. 10
  9. 360
  10. 60
  11. 5
  12. 62
  13. 6
  14. 30
  15. 120
  16. 90
  17. 29
  18. 30
  19. 123
  20. 300
  21. 90
  22. 63
  23. 60
  24. 120
  25. 25
  26. 360
  27. 240
  28. 45
  29. 6
  30. 56
  31. 12
  32. 40
  33. 35
  34. 450
  35. 42
  36. 200
  37. 60
  38. 540
  39. 144
  40. 20

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