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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 538 · 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.Karan takes 75 seconds and Isha 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?
  2. 2.Three temple bells ring every 18, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Ishaan takes 48 seconds and Arjun 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?
  4. 4.Three temple bells ring every 15, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 9, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Two tanks hold 100 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Two tanks hold 360 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Aarav takes 90 seconds and Arjun 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?
  9. 9.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?
  10. 10.Two tanks hold 30 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Zoya takes 30 seconds and Aarav 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?
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 4 or 9.
  13. 13.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Three temple bells ring every 4, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 4, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 40 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Two tanks hold 50 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Dev takes 80 seconds and Isha 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?
  19. 19.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 6 or 8.
  20. 20.Pooja takes 80 seconds and Tara 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?
  21. 21.Three temple bells ring every 30, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Vivaan takes 60 seconds and Meera 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?
  23. 23.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Three temple bells ring every 12, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 180 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.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?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 5 or 8.
  28. 28.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?
  29. 29.Three temple bells ring every 4, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 10 or 4.
  31. 31.Two tanks hold 150 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Karan takes 48 seconds and Sneha 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?
  33. 33.Aarav takes 36 seconds and Diya 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?
  34. 34.Three temple bells ring every 12, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 5, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 8, 15 or 10.
  37. 37.Two tanks hold 45 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Three temple bells ring every 15, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Two tanks hold 90 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 600
  2. 90
  3. 240
  4. 120
  5. 72
  6. 20
  7. 40
  8. 360
  9. 10
  10. 10
  11. 150
  12. 181
  13. 10
  14. 40
  15. 120
  16. 10
  17. 10
  18. 240
  19. 25
  20. 240
  21. 90
  22. 240
  23. 21
  24. 120
  25. 20
  26. 35
  27. 124
  28. 15
  29. 60
  30. 181
  31. 25
  32. 432
  33. 144
  34. 36
  35. 120
  36. 125
  37. 15
  38. 60
  39. 15
  40. 15

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