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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 313 · 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 20, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Priya takes 30 seconds and Rohan 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?
  3. 3.Tara takes 48 seconds and Sneha 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?
  4. 4.Two tanks hold 90 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.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?
  6. 6.Two tanks hold 160 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.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?
  8. 8.Three temple bells ring every 5, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 4, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Pooja takes 60 seconds and Zoya 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?
  11. 11.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?
  12. 12.A hall floor is 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Kabir takes 90 seconds and Aarav 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?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 12 or 10.
  15. 15.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 6 or 5.
  16. 16.Two tanks hold 210 litres and 150 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 24, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Ananya takes 30 seconds and Nisha 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?
  19. 19.Isha takes 54 seconds and Zoya 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?
  20. 20.Three temple bells ring every 30, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 15 or 4.
  22. 22.Two tanks hold 90 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Three temple bells ring every 8, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 270 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Farhan takes 72 seconds and Isha 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?
  27. 27.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.A hall floor is 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Two tanks hold 45 litres and 60 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 12 that leaves a remainder of 1 when divided by 8, 3 or 12.
  32. 32.Two tanks hold 350 litres and 100 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 9 that leaves a remainder of 1 when divided by 6, 5 or 9.
  34. 34.Three temple bells ring every 6, 4 and 9 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 2 when divided by 9, 8 or 12.
  36. 36.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Meera takes 40 seconds and Vivaan 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?
  38. 38.Two tanks hold 315 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Two tanks hold 35 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 4 or 3.

Answer key

  1. 60
  2. 270
  3. 240
  4. 30
  5. 10
  6. 20
  7. 40
  8. 30
  9. 72
  10. 240
  11. 120
  12. 30
  13. 360
  14. 62
  15. 92
  16. 30
  17. 120
  18. 180
  19. 270
  20. 120
  21. 61
  22. 30
  23. 120
  24. 30
  25. 12
  26. 360
  27. 42
  28. 6
  29. 56
  30. 15
  31. 25
  32. 50
  33. 91
  34. 36
  35. 74
  36. 14
  37. 360
  38. 45
  39. 5
  40. 26

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