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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 114 · 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 4 when divided by 5, 8 or 10.
  2. 2.Three temple bells ring every 15, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Diya takes 60 seconds and Kavya 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?
  5. 5.A hall floor is 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Three temple bells ring every 8, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 9, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 5.
  10. 10.Two tanks hold 125 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 5 or 8.
  12. 12.Three temple bells ring every 6, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Rahul takes 60 seconds and Meera 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?
  14. 14.Three temple bells ring every 4, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 8 or 15.
  16. 16.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Three temple bells ring every 24, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Rahul takes 60 seconds and Ishaan 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?
  20. 20.Two tanks hold 120 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 10, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 10 or 15.
  23. 23.Ananya takes 36 seconds and Rohan 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?
  24. 24.Two tanks hold 15 litres and 20 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 15 that leaves a remainder of 3 when divided by 6, 10 or 15.
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 5 or 12.
  27. 27.Two tanks hold 100 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 5 or 15.
  30. 30.Three temple bells ring every 9, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 30, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 12, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 240 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Two tanks hold 40 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 3 or 12.
  36. 36.Three temple bells ring every 6, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Aarav takes 30 seconds and Farhan 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?
  38. 38.Kavya takes 50 seconds and Aditya 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?
  39. 39.Find the smallest number bigger than 6 that leaves a remainder of 3 when divided by 5, 4 or 6.
  40. 40.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 5, 9 or 3.

Answer key

  1. 44
  2. 60
  3. 15
  4. 120
  5. 30
  6. 21
  7. 120
  8. 72
  9. 32
  10. 25
  11. 122
  12. 30
  13. 180
  14. 60
  15. 123
  16. 14
  17. 72
  18. 10
  19. 300
  20. 40
  21. 30
  22. 33
  23. 108
  24. 5
  25. 33
  26. 61
  27. 25
  28. 10
  29. 32
  30. 90
  31. 60
  32. 60
  33. 30
  34. 10
  35. 61
  36. 120
  37. 240
  38. 450
  39. 63
  40. 47

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