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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 222 · 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).

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  1. 1.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Three temple bells ring every 30, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 8, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Aarav takes 48 seconds and Kavya 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?
  5. 5.Saanvi takes 36 seconds and Pooja 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?
  6. 6.Three temple bells ring every 8, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 9, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 10, 12 or 6.
  9. 9.Two tanks hold 450 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.Three temple bells ring every 15, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Meera takes 90 seconds and Nisha 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.Saanvi takes 90 seconds and Meera 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?
  13. 13.Two tanks hold 80 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Three temple bells ring every 4, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Manav takes 30 seconds and Arjun 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?
  16. 16.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 5 or 8.
  17. 17.Diya takes 80 seconds and Aditya 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?
  18. 18.Three temple bells ring every 9, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 4 or 12.
  20. 20.Two tanks hold 120 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Saanvi takes 45 seconds and Meera 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?
  22. 22.Arjun takes 54 seconds and Nisha 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?
  23. 23.Two tanks hold 45 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 6, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Ishaan takes 36 seconds and Saanvi 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?
  26. 26.A hall floor is 280 cm long and 120 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 2 when divided by 8, 9 or 12.
  28. 28.Three temple bells ring every 6, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Aditya takes 50 seconds and Priya 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?
  31. 31.Three temple bells ring every 30, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 15, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 120 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Three temple bells ring every 18, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 3.
  36. 36.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 6 when divided by 10, 9 or 12.
  38. 38.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 9 or 4.
  39. 39.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 8 or 4.
  40. 40.Three temple bells ring every 20, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 12
  2. 90
  3. 40
  4. 144
  5. 144
  6. 120
  7. 90
  8. 63
  9. 50
  10. 60
  11. 450
  12. 450
  13. 10
  14. 120
  15. 240
  16. 41
  17. 720
  18. 72
  19. 26
  20. 30
  21. 180
  22. 270
  23. 5
  24. 24
  25. 108
  26. 21
  27. 74
  28. 60
  29. 50
  30. 300
  31. 60
  32. 120
  33. 40
  34. 90
  35. 37
  36. 24
  37. 186
  38. 181
  39. 42
  40. 120

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