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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 177 · 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 10, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 12, 15 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 18, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 12, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Two tanks hold 40 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Sneha takes 45 seconds and Manav 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?
  7. 7.Three temple bells ring every 4, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.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?
  9. 9.Aarav takes 30 seconds and Zoya 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?
  10. 10.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?
  11. 11.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Saanvi takes 45 seconds and Meera 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?
  13. 13.Three temple bells ring every 30, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 30, 8 and 6 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 3 when divided by 5, 6 or 12.
  16. 16.Two tanks hold 80 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Ananya takes 36 seconds and Tara 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?
  18. 18.Two tanks hold 225 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Two tanks hold 270 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.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?
  21. 21.Three temple bells ring every 18, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 4 or 6.
  23. 23.Zoya takes 75 seconds and Nisha 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?
  24. 24.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 18, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 6.
  28. 28.Three temple bells ring every 4, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 210 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 9 or 4.
  31. 31.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 4.
  32. 32.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.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?
  34. 34.Three temple bells ring every 20, 12 and 4 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 5, 12 or 3.
  36. 36.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Two tanks hold 15 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 8, 4 or 10.
  40. 40.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?

Answer key

  1. 90
  2. 60
  3. 90
  4. 60
  5. 20
  6. 450
  7. 36
  8. 6
  9. 360
  10. 50
  11. 35
  12. 360
  13. 60
  14. 120
  15. 63
  16. 20
  17. 180
  18. 25
  19. 45
  20. 12
  21. 90
  22. 13
  23. 450
  24. 6
  25. 21
  26. 90
  27. 13
  28. 120
  29. 30
  30. 183
  31. 37
  32. 14
  33. 24
  34. 60
  35. 61
  36. 15
  37. 10
  38. 5
  39. 43
  40. 6

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