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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 424 · 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 15, 6 and 4 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 6 that leaves a remainder of 1 when divided by 4, 6 or 5.
  3. 3.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 4 or 5.
  4. 4.Three temple bells ring every 5, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 9 or 3.
  6. 6.Karan takes 45 seconds and Zoya 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?
  7. 7.Two tanks hold 250 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Two tanks hold 80 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Tara takes 60 seconds and Farhan 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?
  10. 10.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Sneha takes 36 seconds and Zoya 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?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 5 or 12.
  13. 13.Two tanks hold 200 litres and 280 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 5, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 5 or 3.
  16. 16.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?
  17. 17.Three temple bells ring every 20, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 18, 9 and 8 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, 12 or 10.
  20. 20.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 6, 12 or 15.
  21. 21.Three temple bells ring every 24, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 30, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 150 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Two tanks hold 10 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 6.
  26. 26.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?
  27. 27.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 4 or 8.
  28. 28.Kavya takes 60 seconds and Arjun 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?
  29. 29.Saanvi takes 72 seconds and Rahul 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?
  30. 30.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Zoya takes 90 seconds and Nisha 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?
  32. 32.Vivaan takes 90 seconds and Diya 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?
  33. 33.Three temple bells ring every 15, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 9 or 10.
  35. 35.Two tanks hold 105 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 15, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 12, 5 or 15.
  38. 38.Aditya takes 30 seconds and Ishaan 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?
  39. 39.Ishaan takes 30 seconds and Saanvi 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?
  40. 40.Vivaan takes 45 seconds and Rohan 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?

Answer key

  1. 60
  2. 61
  3. 41
  4. 30
  5. 73
  6. 180
  7. 50
  8. 10
  9. 300
  10. 12
  11. 360
  12. 61
  13. 40
  14. 60
  15. 62
  16. 21
  17. 60
  18. 72
  19. 122
  20. 64
  21. 120
  22. 60
  23. 50
  24. 5
  25. 37
  26. 42
  27. 74
  28. 360
  29. 360
  30. 10
  31. 720
  32. 360
  33. 120
  34. 91
  35. 15
  36. 60
  37. 64
  38. 180
  39. 150
  40. 360

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