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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 340 · 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.Three temple bells ring every 12, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 9 or 5.
  3. 3.Arjun takes 48 seconds and Tara 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?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 12 or 15.
  5. 5.Three temple bells ring every 15, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Ananya takes 48 seconds and Dev 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?
  8. 8.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 12.
  9. 9.Find the smallest number bigger than 9 that leaves a remainder of 4 when divided by 9, 6 or 8.
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 8, 10 or 15.
  11. 11.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 3 or 9.
  13. 13.Two tanks hold 135 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 3.
  15. 15.Three temple bells ring every 9, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Rohan takes 40 seconds and Sneha 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?
  17. 17.Pooja takes 75 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?
  18. 18.Saanvi takes 30 seconds and Manav 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?
  19. 19.Three temple bells ring every 30, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 6, 10 or 15.
  21. 21.Two tanks hold 10 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.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?
  23. 23.Three temple bells ring every 12, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 35 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 9, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 160 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Tara takes 60 seconds and Aditya 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?
  28. 28.Ananya takes 36 seconds and Meera 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?
  29. 29.Three temple bells ring every 8, 30 and 24 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 15 that leaves a remainder of 3 when divided by 12, 4 or 15.
  31. 31.Three temple bells ring every 8, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 18, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 8, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 18, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.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?
  36. 36.Kavya takes 60 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?
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 9 or 6.
  38. 38.Three temple bells ring every 9, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 10.
  40. 40.Three temple bells ring every 9, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 120
  2. 48
  3. 240
  4. 62
  5. 120
  6. 15
  7. 240
  8. 122
  9. 76
  10. 127
  11. 20
  12. 20
  13. 45
  14. 13
  15. 90
  16. 360
  17. 300
  18. 150
  19. 120
  20. 33
  21. 5
  22. 6
  23. 60
  24. 5
  25. 72
  26. 20
  27. 180
  28. 108
  29. 120
  30. 63
  31. 120
  32. 72
  33. 72
  34. 72
  35. 60
  36. 300
  37. 93
  38. 90
  39. 62
  40. 36

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