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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 545 · 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 4 when divided by 9, 5 or 15.
  2. 2.Ishaan takes 48 seconds and Arjun 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?
  3. 3.Three temple bells ring every 4, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 8 or 3.
  5. 5.Isha takes 54 seconds and Pooja 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?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 10 or 6.
  7. 7.Sneha takes 50 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?
  8. 8.Two tanks hold 150 litres and 400 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 120 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 12 or 6.
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 10.
  13. 13.Two tanks hold 400 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 12 or 15.
  15. 15.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Three temple bells ring every 20, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Two tanks hold 45 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.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?
  19. 19.A hall floor is 225 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 6, 4 or 8.
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 10 or 6.
  22. 22.Two tanks hold 160 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Isha takes 48 seconds and Priya 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?
  24. 24.Rohan takes 36 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?
  25. 25.Sneha takes 60 seconds and Rahul 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?
  26. 26.A hall floor is 100 cm long and 40 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 8, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 15, 10 or 8.
  29. 29.Rohan takes 40 seconds and Tara 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?
  30. 30.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 5.
  32. 32.Three temple bells ring every 24, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.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?
  34. 34.Three temple bells ring every 8, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 10, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Dev takes 40 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?
  37. 37.Three temple bells ring every 24, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 4 or 15.
  39. 39.Aarav takes 30 seconds and Tara 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?
  40. 40.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?

Answer key

  1. 49
  2. 240
  3. 120
  4. 122
  5. 216
  6. 32
  7. 150
  8. 50
  9. 40
  10. 6
  11. 14
  12. 31
  13. 50
  14. 61
  15. 28
  16. 60
  17. 15
  18. 6
  19. 20
  20. 27
  21. 62
  22. 40
  23. 240
  24. 360
  25. 120
  26. 10
  27. 72
  28. 126
  29. 360
  30. 21
  31. 62
  32. 72
  33. 21
  34. 40
  35. 120
  36. 120
  37. 120
  38. 63
  39. 150
  40. 56

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