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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 18 · 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 8, 18 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 15, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Kabir takes 80 seconds and Isha 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?
  4. 4.Three temple bells ring every 10, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Diya takes 45 seconds and Meera 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.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Kabir takes 80 seconds and Dev 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?
  8. 8.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 8 or 15.
  9. 9.Two tanks hold 75 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Two tanks hold 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.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?
  12. 12.Three temple bells ring every 8, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Ishaan takes 48 seconds and Kavya 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?
  14. 14.Three temple bells ring every 12, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.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?
  16. 16.Saanvi takes 48 seconds and Arjun takes 90 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.Two tanks hold 60 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 30, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 8, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.A hall floor is 400 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Two tanks hold 50 litres and 40 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 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.A hall floor is 480 cm long and 180 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 24, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Aditya takes 48 seconds and Arjun 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?
  27. 27.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 6, 5 or 9.
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 10 or 12.
  29. 29.Three temple bells ring every 5, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Nisha takes 60 seconds and Isha 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.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 8 or 6.
  32. 32.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?
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 6.
  34. 34.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?
  35. 35.Three temple bells ring every 30, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 150 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Find the smallest number bigger than 8 that leaves a remainder of 4 when divided by 6, 5 or 8.
  38. 38.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?
  39. 39.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Manav takes 75 seconds and Ananya 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?

Answer key

  1. 72
  2. 90
  3. 720
  4. 90
  5. 360
  6. 15
  7. 720
  8. 124
  9. 25
  10. 10
  11. 120
  12. 120
  13. 432
  14. 36
  15. 10
  16. 720
  17. 20
  18. 120
  19. 120
  20. 40
  21. 10
  22. 12
  23. 24
  24. 120
  25. 12
  26. 720
  27. 93
  28. 63
  29. 40
  30. 300
  31. 26
  32. 40
  33. 32
  34. 15
  35. 120
  36. 30
  37. 124
  38. 40
  39. 42
  40. 150

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