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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 270 · 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.Farhan takes 45 seconds and Karan 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?
  2. 2.Zoya takes 45 seconds and Kabir 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?
  3. 3.Three temple bells ring every 12, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 4, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.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?
  6. 6.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?
  7. 7.A hall floor is 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Meera takes 36 seconds and Manav 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?
  12. 12.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 6 or 4.
  14. 14.Dev takes 30 seconds and Zoya 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?
  15. 15.Zoya takes 80 seconds and Pooja 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?
  16. 16.Meera takes 90 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?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 3.
  18. 18.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 8 or 6.
  19. 19.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?
  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.Find the smallest number bigger than 10 that leaves a remainder of 5 when divided by 10, 6 or 9.
  22. 22.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?
  23. 23.Diya takes 60 seconds and Kabir 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?
  24. 24.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?
  25. 25.Two tanks hold 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 6, 12 or 8.
  27. 27.Three temple bells ring every 5, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.A hall floor is 120 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 5 when divided by 15, 10 or 6.
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 4 or 6.
  31. 31.Three temple bells ring every 10, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 10 or 3.
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 6.
  34. 34.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 3.
  35. 35.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 9, 6 or 10.
  36. 36.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 9 or 4.
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 9 or 3.
  38. 38.Manav takes 48 seconds and Nisha 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?
  39. 39.Nisha takes 90 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?
  40. 40.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 270
  2. 360
  3. 24
  4. 60
  5. 15
  6. 14
  7. 30
  8. 28
  9. 40
  10. 30
  11. 180
  12. 21
  13. 38
  14. 120
  15. 240
  16. 450
  17. 61
  18. 25
  19. 15
  20. 12
  21. 95
  22. 12
  23. 240
  24. 6
  25. 10
  26. 26
  27. 120
  28. 12
  29. 35
  30. 62
  31. 60
  32. 121
  33. 32
  34. 37
  35. 94
  36. 38
  37. 47
  38. 144
  39. 450
  40. 14

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