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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 349 · 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 8 that leaves a remainder of 2 when divided by 8, 5 or 4.
  2. 2.Three temple bells ring every 20, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Two tanks hold 315 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Three temple bells ring every 12, 20 and 24 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 10 that leaves a remainder of 2 when divided by 6, 4 or 10.
  6. 6.Three temple bells ring every 24, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 20 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  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.Pooja takes 50 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?
  11. 11.Three temple bells ring every 15, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Two tanks hold 40 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Diya takes 40 seconds and Vivaan 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?
  15. 15.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Karan takes 45 seconds and Aditya 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?
  17. 17.Two tanks hold 280 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Rahul takes 40 seconds and Aarav 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?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 12 or 15.
  20. 20.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?
  21. 21.Two tanks hold 40 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Two tanks hold 80 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.Sneha takes 90 seconds and Saanvi 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?
  24. 24.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 6, 8 or 5.
  25. 25.Two tanks hold 120 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Two tanks hold 35 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Saanvi takes 90 seconds and Aarav 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?
  28. 28.Two tanks hold 180 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.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?
  30. 30.Two tanks hold 90 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 4 or 10.
  32. 32.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?
  33. 33.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 5 or 4.
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 6.
  35. 35.Two tanks hold 405 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.A hall floor is 350 cm long and 300 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 30, 4 and 24 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 9 that leaves a remainder of 1 when divided by 9, 3 or 4.
  39. 39.Three temple bells ring every 12, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 5, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 42
  2. 120
  3. 45
  4. 120
  5. 62
  6. 120
  7. 10
  8. 56
  9. 40
  10. 150
  11. 90
  12. 10
  13. 20
  14. 120
  15. 14
  16. 180
  17. 40
  18. 120
  19. 62
  20. 12
  21. 20
  22. 10
  23. 360
  24. 123
  25. 15
  26. 5
  27. 720
  28. 30
  29. 72
  30. 15
  31. 62
  32. 12
  33. 62
  34. 13
  35. 45
  36. 42
  37. 120
  38. 37
  39. 120
  40. 60

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