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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 372 · 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.Aarav takes 80 seconds and Rohan 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?
  2. 2.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 10 or 5.
  3. 3.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Three temple bells ring every 5, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Zoya takes 36 seconds and Pooja 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?
  6. 6.Three temple bells ring every 6, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.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?
  8. 8.Three temple bells ring every 18, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Karan takes 36 seconds and Ishaan 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?
  10. 10.Two tanks hold 240 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.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?
  12. 12.Isha takes 45 seconds and Aditya 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?
  13. 13.A hall floor is 360 cm long and 315 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 10 that leaves a remainder of 1 when divided by 10, 8 or 4.
  15. 15.Rahul takes 48 seconds and Vivaan 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?
  16. 16.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 3.
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 12 or 15.
  18. 18.Two tanks hold 100 litres and 75 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 12 that leaves a remainder of 2 when divided by 5, 12 or 6.
  20. 20.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?
  21. 21.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Three temple bells ring every 12, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 5, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 140 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Farhan takes 48 seconds and Pooja 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?
  26. 26.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 10 or 15.
  28. 28.A hall floor is 200 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Two tanks hold 250 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Two tanks hold 140 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Rahul takes 30 seconds and Saanvi 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?
  32. 32.Dev takes 45 seconds and Kabir 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?
  33. 33.Three temple bells ring every 20, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 20, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 10 or 3.
  36. 36.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?
  37. 37.Karan takes 36 seconds and Tara 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?
  38. 38.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 6 or 9.
  39. 39.Three temple bells ring every 6, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 30, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 240
  2. 31
  3. 56
  4. 60
  5. 360
  6. 72
  7. 50
  8. 72
  9. 180
  10. 30
  11. 35
  12. 90
  13. 56
  14. 41
  15. 240
  16. 32
  17. 182
  18. 25
  19. 62
  20. 50
  21. 30
  22. 24
  23. 20
  24. 20
  25. 240
  26. 40
  27. 31
  28. 10
  29. 50
  30. 20
  31. 240
  32. 180
  33. 120
  34. 120
  35. 32
  36. 21
  37. 144
  38. 37
  39. 36
  40. 60

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