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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 62 · 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.Two tanks hold 210 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Two tanks hold 90 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 6, 8 or 10.
  4. 4.Ishaan takes 40 seconds and Aarav 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.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?
  6. 6.Two tanks hold 225 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Three temple bells ring every 30, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Ananya takes 80 seconds and Pooja 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?
  9. 9.Two tanks hold 25 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Meera takes 72 seconds and Farhan 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?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 5.
  12. 12.A hall floor is 360 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Three temple bells ring every 5, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Meera takes 30 seconds and Farhan 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?
  15. 15.Manav takes 45 seconds and Diya 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?
  16. 16.Saanvi takes 30 seconds and Kabir 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?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 4 or 9.
  18. 18.Two tanks hold 180 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 5 or 12.
  20. 20.Nisha takes 36 seconds and Aarav 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?
  21. 21.Tara takes 30 seconds and Diya 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?
  22. 22.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?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 9, 10 or 15.
  24. 24.Rahul takes 30 seconds and Sneha 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?
  25. 25.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  26. 26.Farhan takes 50 seconds and Nisha 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?
  27. 27.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?
  28. 28.A hall floor is 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Arjun takes 72 seconds and Manav 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?
  30. 30.Two tanks hold 140 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 5.
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 8 or 10.
  33. 33.Three temple bells ring every 24, 30 and 12 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 2 when divided by 10, 3 or 9.
  35. 35.Three temple bells ring every 15, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 4.
  37. 37.Two tanks hold 135 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Three temple bells ring every 15, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 30
  2. 10
  3. 124
  4. 360
  5. 24
  6. 25
  7. 120
  8. 240
  9. 5
  10. 360
  11. 16
  12. 24
  13. 60
  14. 120
  15. 180
  16. 90
  17. 38
  18. 20
  19. 63
  20. 180
  21. 240
  22. 15
  23. 97
  24. 240
  25. 31
  26. 300
  27. 5
  28. 30
  29. 144
  30. 20
  31. 46
  32. 122
  33. 120
  34. 92
  35. 60
  36. 25
  37. 45
  38. 120
  39. 20
  40. 14

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