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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 106 · 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 12 that leaves a remainder of 3 when divided by 4, 12 or 9.
  2. 2.Three temple bells ring every 30, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Saanvi takes 75 seconds and Ishaan 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?
  4. 4.Nisha 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?
  5. 5.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.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?
  7. 7.Two tanks hold 90 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Two tanks hold 75 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 4 or 5.
  10. 10.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Three temple bells ring every 6, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 4 or 5.
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 9 or 5.
  16. 16.Saanvi takes 50 seconds and Diya 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?
  17. 17.Manav takes 45 seconds and Tara 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?
  18. 18.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 5, 3 or 8.
  20. 20.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.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?
  22. 22.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Karan takes 45 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?
  24. 24.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Three temple bells ring every 15, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Manav takes 45 seconds and Ishaan 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?
  27. 27.Three temple bells ring every 10, 6 and 20 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 10 that leaves a remainder of 1 when divided by 3, 6 or 10.
  29. 29.Three temple bells ring every 12, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 6 or 10.
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 6, 12 or 9.
  32. 32.Three temple bells ring every 15, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Tara takes 48 seconds and Meera 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?
  34. 34.Two tanks hold 350 litres and 200 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 10 that leaves a remainder of 1 when divided by 3, 9 or 10.
  36. 36.Farhan takes 72 seconds and Dev 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?
  37. 37.Two tanks hold 30 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Two tanks hold 100 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Meera takes 90 seconds and Rahul 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?

Answer key

  1. 39
  2. 120
  3. 300
  4. 240
  5. 14
  6. 6
  7. 10
  8. 25
  9. 63
  10. 24
  11. 12
  12. 36
  13. 12
  14. 61
  15. 46
  16. 400
  17. 180
  18. 42
  19. 121
  20. 15
  21. 30
  22. 24
  23. 180
  24. 56
  25. 120
  26. 180
  27. 60
  28. 31
  29. 60
  30. 91
  31. 41
  32. 90
  33. 720
  34. 50
  35. 91
  36. 360
  37. 10
  38. 21
  39. 20
  40. 720

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