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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 69 · 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 6 that leaves a remainder of 1 when divided by 4, 6 or 3.
  2. 2.Two tanks hold 60 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Kavya takes 48 seconds and Rohan 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?
  4. 4.Three temple bells ring every 4, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 6 or 8.
  6. 6.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?
  7. 7.Two tanks hold 90 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Two tanks hold 30 litres and 45 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 5, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 320 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Aarav takes 72 seconds and Karan 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?
  12. 12.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Dev takes 36 seconds and Pooja 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?
  14. 14.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Two tanks hold 360 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Two tanks hold 200 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 20, 4 and 30 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 15 that leaves a remainder of 2 when divided by 9, 3 or 15.
  19. 19.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?
  20. 20.Zoya takes 75 seconds and Tara 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?
  21. 21.Three temple bells ring every 15, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Two tanks hold 75 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Two tanks hold 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Two tanks hold 160 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Two tanks hold 350 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Three temple bells ring every 12, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.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?
  28. 28.Aarav takes 50 seconds and Rohan 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?
  29. 29.Nisha takes 80 seconds and Karan 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?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 9 or 6.
  31. 31.Find the smallest number bigger than 6 that leaves a remainder of 3 when divided by 5, 4 or 6.
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 9.
  33. 33.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.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?
  35. 35.Two tanks hold 270 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 5, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 75 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Two tanks hold 135 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.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?
  40. 40.A hall floor is 300 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 13
  2. 15
  3. 720
  4. 60
  5. 25
  6. 40
  7. 10
  8. 15
  9. 60
  10. 40
  11. 144
  12. 40
  13. 180
  14. 20
  15. 45
  16. 50
  17. 60
  18. 47
  19. 40
  20. 225
  21. 120
  22. 15
  23. 10
  24. 40
  25. 50
  26. 60
  27. 15
  28. 150
  29. 240
  30. 94
  31. 63
  32. 46
  33. 6
  34. 10
  35. 30
  36. 60
  37. 25
  38. 15
  39. 12
  40. 20

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