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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 437 · 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 15 that leaves a remainder of 1 when divided by 15, 5 or 9.
  2. 2.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 5, 6 or 8.
  3. 3.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 10 or 6.
  5. 5.Arjun takes 60 seconds and Sneha takes 75 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.Vivaan takes 36 seconds and Dev 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?
  7. 7.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 3 or 8.
  8. 8.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?
  9. 9.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?
  10. 10.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Kabir takes 60 seconds and Diya 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?
  12. 12.Two tanks hold 200 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Ishaan takes 54 seconds and Priya 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?
  14. 14.Rahul takes 40 seconds and Kabir 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?
  15. 15.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?
  16. 16.Two tanks hold 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Pooja takes 54 seconds and Rohan 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?
  18. 18.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 10 or 3.
  19. 19.Two tanks hold 120 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Ishaan takes 50 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?
  21. 21.Three temple bells ring every 12, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 20, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 225 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.Three temple bells ring every 24, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 3 or 6.
  26. 26.Kavya takes 40 seconds and Dev 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?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 6 or 9.
  28. 28.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Manav takes 48 seconds and Saanvi 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?
  30. 30.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 3 or 12.
  31. 31.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?
  32. 32.Priya takes 80 seconds and Vivaan 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?
  33. 33.Dev takes 80 seconds and Ishaan 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?
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 3.
  35. 35.Two tanks hold 120 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 5 or 10.
  37. 37.Three temple bells ring every 6, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Rohan takes 48 seconds and Kavya 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?
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 5 or 15.
  40. 40.Two tanks hold 200 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 46
  2. 121
  3. 42
  4. 63
  5. 300
  6. 720
  7. 25
  8. 120
  9. 90
  10. 12
  11. 120
  12. 50
  13. 270
  14. 360
  15. 5
  16. 20
  17. 216
  18. 62
  19. 30
  20. 450
  21. 60
  22. 60
  23. 25
  24. 120
  25. 32
  26. 360
  27. 95
  28. 12
  29. 144
  30. 13
  31. 15
  32. 720
  33. 240
  34. 31
  35. 15
  36. 21
  37. 72
  38. 720
  39. 122
  40. 25

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