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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 475 · 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.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 5.
  2. 2.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Ishaan takes 60 seconds and Dev 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?
  4. 4.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?
  5. 5.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 10 or 5.
  6. 6.Two tanks hold 135 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 12, 15 or 8.
  8. 8.Two tanks hold 225 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.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?
  10. 10.Three temple bells ring every 6, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Diya takes 54 seconds and Farhan 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?
  12. 12.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?
  13. 13.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Dev takes 30 seconds and Meera 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?
  15. 15.Two tanks hold 210 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Three temple bells ring every 10, 18 and 6 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 9 that leaves a remainder of 2 when divided by 4, 3 or 9.
  18. 18.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?
  19. 19.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Two tanks hold 250 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Rahul takes 60 seconds and Zoya 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?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 12 or 15.
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 6 or 9.
  24. 24.Priya takes 36 seconds and Ananya 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?
  25. 25.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 3.
  26. 26.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Three temple bells ring every 24, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Saanvi takes 40 seconds and Vivaan 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?
  29. 29.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 4 or 3.
  30. 30.Two tanks hold 50 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 15, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Saanvi takes 72 seconds and Nisha 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?
  33. 33.Ananya 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?
  34. 34.Ananya takes 45 seconds and Priya 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?
  35. 35.Three temple bells ring every 15, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.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?
  37. 37.Three temple bells ring every 6, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Two tanks hold 225 litres and 175 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 15 that leaves a remainder of 3 when divided by 9, 4 or 15.
  40. 40.Sneha takes 36 seconds and Ishaan 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?

Answer key

  1. 46
  2. 24
  3. 180
  4. 42
  5. 91
  6. 15
  7. 124
  8. 25
  9. 5
  10. 60
  11. 540
  12. 40
  13. 10
  14. 360
  15. 30
  16. 90
  17. 38
  18. 35
  19. 20
  20. 50
  21. 180
  22. 61
  23. 94
  24. 180
  25. 37
  26. 56
  27. 120
  28. 240
  29. 13
  30. 25
  31. 60
  32. 360
  33. 360
  34. 270
  35. 30
  36. 28
  37. 36
  38. 25
  39. 183
  40. 144

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