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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 516 · 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 2 when divided by 3, 9 or 8.
  2. 2.Three temple bells ring every 18, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 20, 8 and 6 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 15 that leaves a remainder of 5 when divided by 10, 8 or 15.
  5. 5.Three temple bells ring every 6, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.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?
  7. 7.Saanvi takes 60 seconds and Kavya 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?
  8. 8.Two tanks hold 225 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Sneha takes 48 seconds and Rohan 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?
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 6 or 15.
  11. 11.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Tara takes 30 seconds and Isha 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?
  13. 13.Kabir takes 40 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.Two tanks hold 120 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Two tanks hold 80 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 9.
  17. 17.Three temple bells ring every 18, 4 and 8 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 3 when divided by 15, 10 or 4.
  19. 19.Ananya takes 30 seconds and Zoya 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?
  20. 20.Two tanks hold 100 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 5 or 6.
  22. 22.Three temple bells ring every 20, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Rahul takes 30 seconds and Tara 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?
  24. 24.Pooja takes 50 seconds and Karan 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?
  25. 25.Three temple bells ring every 10, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 350 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 12, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 4, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.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?
  30. 30.Two tanks hold 270 litres and 60 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, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Two tanks hold 360 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Kabir takes 75 seconds and Priya 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?
  35. 35.Tara takes 54 seconds and Nisha 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?
  36. 36.Two tanks hold 30 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Kavya takes 36 seconds and Tara 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?
  38. 38.Two tanks hold 350 litres and 450 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 12 that leaves a remainder of 1 when divided by 9, 12 or 4.
  40. 40.Two tanks hold 90 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 74
  2. 72
  3. 120
  4. 125
  5. 30
  6. 30
  7. 180
  8. 45
  9. 240
  10. 61
  11. 15
  12. 90
  13. 360
  14. 20
  15. 10
  16. 37
  17. 72
  18. 63
  19. 240
  20. 50
  21. 33
  22. 60
  23. 240
  24. 300
  25. 30
  26. 50
  27. 120
  28. 36
  29. 6
  30. 30
  31. 60
  32. 24
  33. 40
  34. 150
  35. 432
  36. 10
  37. 108
  38. 50
  39. 37
  40. 30

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