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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 259 · 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 5, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 70 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Two tanks hold 140 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.A hall floor is 210 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 4, 5 or 3.
  6. 6.Three temple bells ring every 5, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 20, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 12, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 20 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 10, 9 or 15.
  11. 11.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 5 or 10.
  12. 12.Two tanks hold 75 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 3 or 5.
  14. 14.Two tanks hold 70 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 9 or 6.
  16. 16.Kavya takes 40 seconds and Arjun 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?
  17. 17.Three temple bells ring every 5, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Two tanks hold 135 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Three temple bells ring every 8, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.A hall floor is 300 cm long and 180 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 4, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Nisha takes 45 seconds and Isha 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?
  23. 23.Two tanks hold 450 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 12 or 4.
  26. 26.Rohan takes 90 seconds and Karan 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?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 6.
  28. 28.Two tanks hold 100 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.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?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 9 or 4.
  31. 31.Three temple bells ring every 12, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 18, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 4, 30 and 15 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 9 that leaves a remainder of 3 when divided by 9, 8 or 6.
  35. 35.Three temple bells ring every 5, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 6, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 45 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Two tanks hold 45 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.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?

Answer key

  1. 90
  2. 10
  3. 20
  4. 35
  5. 62
  6. 20
  7. 60
  8. 36
  9. 5
  10. 96
  11. 32
  12. 15
  13. 31
  14. 10
  15. 92
  16. 360
  17. 60
  18. 15
  19. 120
  20. 15
  21. 24
  22. 450
  23. 50
  24. 15
  25. 62
  26. 180
  27. 32
  28. 20
  29. 6
  30. 181
  31. 72
  32. 90
  33. 60
  34. 75
  35. 40
  36. 72
  37. 5
  38. 15
  39. 10
  40. 20

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