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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 237 · 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 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Kavya takes 50 seconds and Rahul 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?
  3. 3.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 6 or 8.
  4. 4.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?
  5. 5.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Arjun takes 72 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?
  7. 7.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?
  8. 8.Three temple bells ring every 4, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.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?
  10. 10.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 5 or 4.
  11. 11.Three temple bells ring every 24, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 9 or 8.
  13. 13.Meera takes 54 seconds and Ananya 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?
  14. 14.Find the smallest number bigger than 9 that leaves a remainder of 5 when divided by 6, 8 or 9.
  15. 15.Isha takes 36 seconds and Kabir 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?
  16. 16.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?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 12 or 4.
  18. 18.Two tanks hold 360 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 10, 9 or 6.
  20. 20.Two tanks hold 350 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 3.
  22. 22.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?
  23. 23.Tara takes 50 seconds and Vivaan 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?
  24. 24.Kabir takes 60 seconds and Sneha 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?
  25. 25.Three temple bells ring every 12, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Ananya takes 60 seconds and Rohan 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?
  27. 27.Three temple bells ring every 30, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 250 litres and 300 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Arjun takes 30 seconds and Kabir 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?
  30. 30.Isha takes 80 seconds and Manav 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?
  31. 31.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Pooja takes 80 seconds and Rohan 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?
  33. 33.Two tanks hold 180 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Three temple bells ring every 6, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 3 or 4.
  37. 37.Three temple bells ring every 10, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 6, 9 or 8.
  39. 39.Meera takes 54 seconds and Karan 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?
  40. 40.Three temple bells ring every 6, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 35
  2. 200
  3. 122
  4. 25
  5. 30
  6. 360
  7. 40
  8. 72
  9. 42
  10. 62
  11. 72
  12. 74
  13. 432
  14. 77
  15. 360
  16. 25
  17. 37
  18. 40
  19. 94
  20. 50
  21. 37
  22. 40
  23. 150
  24. 180
  25. 60
  26. 180
  27. 90
  28. 50
  29. 120
  30. 720
  31. 6
  32. 240
  33. 20
  34. 36
  35. 24
  36. 38
  37. 90
  38. 75
  39. 108
  40. 24

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