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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 370 · 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.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?
  2. 2.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 4 or 6.
  3. 3.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Nisha takes 90 seconds and Diya 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?
  6. 6.Three temple bells ring every 6, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 5, 4 or 3.
  8. 8.Two tanks hold 140 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Rahul takes 30 seconds and Priya 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?
  10. 10.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Two tanks hold 105 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Priya takes 60 seconds and Arjun 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?
  13. 13.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?
  14. 14.Two tanks hold 60 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Rohan takes 54 seconds and Diya 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?
  16. 16.Three temple bells ring every 24, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 20, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Kavya takes 90 seconds and Aarav 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?
  19. 19.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 8 or 10.
  20. 20.Two tanks hold 45 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Two tanks hold 240 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Three temple bells ring every 15, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 8, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Meera takes 40 seconds and Ananya 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?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 12 or 15.
  26. 26.Isha takes 54 seconds and Pooja 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?
  27. 27.Kavya takes 72 seconds and Farhan 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?
  28. 28.Three temple bells ring every 24, 15 and 30 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 15 that leaves a remainder of 1 when divided by 8, 3 or 15.
  30. 30.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Pooja takes 80 seconds and Karan 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?
  32. 32.Two tanks hold 100 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Tara takes 75 seconds and Sneha 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.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?
  35. 35.Diya takes 45 seconds and Sneha 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?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 5, 12 or 9.
  37. 37.Three temple bells ring every 30, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Meera takes 60 seconds and Nisha 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?

Answer key

  1. 10
  2. 13
  3. 10
  4. 56
  5. 450
  6. 90
  7. 61
  8. 20
  9. 360
  10. 24
  11. 15
  12. 180
  13. 6
  14. 20
  15. 108
  16. 120
  17. 60
  18. 180
  19. 121
  20. 15
  21. 40
  22. 60
  23. 120
  24. 360
  25. 62
  26. 216
  27. 216
  28. 120
  29. 121
  30. 35
  31. 720
  32. 50
  33. 150
  34. 30
  35. 720
  36. 184
  37. 90
  38. 10
  39. 42
  40. 540

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