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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 280 · 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.Meera takes 54 seconds and Tara 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?
  2. 2.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 5, 6 or 3.
  3. 3.Two tanks hold 50 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.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?
  5. 5.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Three temple bells ring every 30, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 24, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Three temple bells ring every 6, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 135 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Kabir takes 80 seconds and Saanvi 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?
  12. 12.Three temple bells ring every 9, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Isha takes 80 seconds and Rohan 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?
  14. 14.Three temple bells ring every 5, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Aditya takes 80 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?
  16. 16.Three temple bells ring every 6, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 5 or 9.
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 6 or 5.
  19. 19.Two tanks hold 225 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Priya takes 50 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?
  21. 21.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 9, 12 or 4.
  22. 22.Two tanks hold 35 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Aarav takes 45 seconds and Nisha 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.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 8 or 3.
  25. 25.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 4, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 15, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 25 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Two tanks hold 125 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Rohan takes 90 seconds and Ishaan 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?
  31. 31.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?
  32. 32.A hall floor is 300 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Three temple bells ring every 9, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Sneha takes 40 seconds and Farhan 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?
  35. 35.Two tanks hold 35 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 9 or 5.
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 5.
  38. 38.Two tanks hold 100 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Nisha takes 48 seconds and Diya 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?
  40. 40.Vivaan takes 80 seconds and Manav 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. 270
  2. 31
  3. 10
  4. 120
  5. 20
  6. 60
  7. 120
  8. 28
  9. 120
  10. 45
  11. 720
  12. 72
  13. 720
  14. 120
  15. 720
  16. 60
  17. 47
  18. 33
  19. 25
  20. 150
  21. 39
  22. 5
  23. 90
  24. 25
  25. 14
  26. 60
  27. 60
  28. 5
  29. 25
  30. 450
  31. 12
  32. 20
  33. 72
  34. 600
  35. 5
  36. 184
  37. 61
  38. 25
  39. 432
  40. 240

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