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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 311 · 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, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 200 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 5.
  4. 4.Three temple bells ring every 6, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Vivaan takes 40 seconds and Arjun 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.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?
  7. 7.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  8. 8.Ananya takes 45 seconds and Priya 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?
  9. 9.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?
  10. 10.Two tanks hold 25 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Diya takes 54 seconds and Kavya 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?
  12. 12.Pooja takes 80 seconds and Meera 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?
  13. 13.Three temple bells ring every 30, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 8, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.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?
  17. 17.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Two tanks hold 400 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Three temple bells ring every 4, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 24, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Isha takes 36 seconds and Kavya 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?
  24. 24.Karan takes 90 seconds and Tara 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?
  25. 25.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Kavya takes 45 seconds and Aarav 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?
  27. 27.Diya takes 75 seconds and Meera 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?
  28. 28.Three temple bells ring every 24, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 5, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Two tanks hold 300 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Karan takes 40 seconds and Arjun 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?
  32. 32.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 5 or 3.
  34. 34.A hall floor is 175 cm long and 75 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 15, 12 or 4.
  36. 36.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 5.
  37. 37.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 4 or 5.
  38. 38.Two tanks hold 80 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Rohan takes 36 seconds and Karan 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?
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 12 or 15.

Answer key

  1. 72
  2. 40
  3. 122
  4. 60
  5. 360
  6. 21
  7. 31
  8. 360
  9. 12
  10. 5
  11. 270
  12. 720
  13. 90
  14. 72
  15. 15
  16. 56
  17. 14
  18. 50
  19. 120
  20. 72
  21. 24
  22. 21
  23. 180
  24. 720
  25. 10
  26. 450
  27. 150
  28. 120
  29. 120
  30. 50
  31. 120
  32. 10
  33. 46
  34. 21
  35. 62
  36. 31
  37. 41
  38. 40
  39. 108
  40. 61

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