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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 459 · 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 30 seconds and Arjun 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?
  2. 2.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 8, 5 or 12.
  3. 3.Two tanks hold 120 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Two tanks hold 180 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Three temple bells ring every 18, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 8, 6 and 9 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 10 that leaves a remainder of 1 when divided by 10, 3 or 8.
  8. 8.Zoya takes 60 seconds and Nisha 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.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 6, 4 or 10.
  10. 10.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 4.
  11. 11.Three temple bells ring every 18, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.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?
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 6 or 4.
  14. 14.Sneha takes 36 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?
  15. 15.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?
  16. 16.Two tanks hold 180 litres and 150 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 15 that leaves a remainder of 3 when divided by 15, 9 or 12.
  18. 18.Three temple bells ring every 5, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Kabir takes 50 seconds and Vivaan 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?
  20. 20.Three temple bells ring every 8, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Priya takes 40 seconds and Nisha 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?
  23. 23.Three temple bells ring every 10, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 30, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 6, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 8, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 180 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 15, 8 and 4 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 4, 8 or 15.
  30. 30.Ishaan takes 90 seconds and Kabir 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?
  31. 31.Ishaan takes 90 seconds and Nisha takes 50 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.Three temple bells ring every 24, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 100 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 9 or 15.
  35. 35.Diya takes 60 seconds and Kabir 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 15 that leaves a remainder of 3 when divided by 4, 12 or 15.
  37. 37.Three temple bells ring every 6, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Three temple bells ring every 5, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Two tanks hold 90 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Kabir takes 90 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?

Answer key

  1. 150
  2. 123
  3. 20
  4. 20
  5. 90
  6. 72
  7. 121
  8. 120
  9. 63
  10. 62
  11. 90
  12. 40
  13. 37
  14. 180
  15. 50
  16. 30
  17. 183
  18. 20
  19. 150
  20. 40
  21. 21
  22. 120
  23. 60
  24. 120
  25. 90
  26. 72
  27. 45
  28. 120
  29. 121
  30. 270
  31. 450
  32. 120
  33. 50
  34. 181
  35. 240
  36. 63
  37. 24
  38. 30
  39. 30
  40. 180

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