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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 66 · 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.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 8 or 10.
  2. 2.Three temple bells ring every 10, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 15, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.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?
  5. 5.Nisha takes 80 seconds and Kabir 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?
  6. 6.Kabir takes 60 seconds and Tara 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?
  7. 7.Kavya takes 40 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?
  8. 8.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Dev takes 30 seconds and Diya 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?
  10. 10.Aarav takes 90 seconds and Kabir 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?
  11. 11.A hall floor is 150 cm long and 100 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 12 that leaves a remainder of 5 when divided by 9, 8 or 12.
  13. 13.Two tanks hold 400 litres and 450 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 15 that leaves a remainder of 2 when divided by 10, 3 or 15.
  15. 15.Kabir takes 40 seconds and Priya 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?
  16. 16.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?
  17. 17.Three temple bells ring every 10, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 5, 12 or 8.
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 12 or 4.
  20. 20.Tara takes 90 seconds and Manav 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?
  21. 21.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 5 or 6.
  22. 22.Aarav takes 48 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?
  23. 23.Two tanks hold 225 litres and 175 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 60 litres and 105 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 15, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 280 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 12 or 10.
  28. 28.Priya takes 54 seconds and Saanvi 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?
  29. 29.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 8 or 12.
  30. 30.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Kabir takes 60 seconds and Arjun 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?
  32. 32.Two tanks hold 120 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 9.
  34. 34.Two tanks hold 80 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Two tanks hold 135 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 5, 12 or 6.
  37. 37.Three temple bells ring every 18, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 5, 3 or 4.
  39. 39.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 3 or 4.
  40. 40.Three temple bells ring every 6, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 42
  2. 120
  3. 60
  4. 10
  5. 720
  6. 180
  7. 120
  8. 10
  9. 90
  10. 180
  11. 6
  12. 77
  13. 50
  14. 32
  15. 360
  16. 50
  17. 120
  18. 124
  19. 63
  20. 450
  21. 93
  22. 240
  23. 25
  24. 15
  25. 120
  26. 40
  27. 61
  28. 270
  29. 25
  30. 35
  31. 240
  32. 40
  33. 91
  34. 20
  35. 15
  36. 64
  37. 72
  38. 61
  39. 25
  40. 60

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