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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 217 · 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 10 that leaves a remainder of 1 when divided by 8, 10 or 3.
  2. 2.Vivaan takes 40 seconds and Karan 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?
  3. 3.Three temple bells ring every 20, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 70 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Three temple bells ring every 5, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 6, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.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?
  8. 8.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 15 or 5.
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 3 or 12.
  10. 10.Three temple bells ring every 20, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 120 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 3 or 10.
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 4 or 15.
  14. 14.Tara takes 60 seconds and Ishaan 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?
  15. 15.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 4 or 12.
  16. 16.Aarav takes 90 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?
  17. 17.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Two tanks hold 35 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.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?
  20. 20.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Three temple bells ring every 6, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Zoya takes 45 seconds and Priya 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?
  23. 23.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?
  24. 24.Two tanks hold 50 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 3 or 9.
  26. 26.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 6, 8 or 4.
  27. 27.Three temple bells ring every 12, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 20, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 5 or 8.
  30. 30.Three temple bells ring every 15, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Ananya takes 60 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?
  32. 32.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?
  33. 33.Zoya takes 45 seconds and Rahul 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?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 12 or 4.
  35. 35.Rahul takes 40 seconds and Rohan 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?
  36. 36.Two tanks hold 25 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Arjun takes 54 seconds and Zoya 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?
  38. 38.Two tanks hold 180 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Two tanks hold 150 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 9 or 6.

Answer key

  1. 121
  2. 600
  3. 60
  4. 10
  5. 90
  6. 60
  7. 12
  8. 47
  9. 61
  10. 60
  11. 30
  12. 61
  13. 61
  14. 240
  15. 61
  16. 180
  17. 6
  18. 5
  19. 40
  20. 12
  21. 60
  22. 90
  23. 15
  24. 25
  25. 38
  26. 26
  27. 60
  28. 60
  29. 43
  30. 120
  31. 240
  32. 15
  33. 90
  34. 61
  35. 200
  36. 5
  37. 540
  38. 20
  39. 25
  40. 39

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