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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 520 · 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 18, 10 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.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?
  3. 3.Meera takes 60 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?
  4. 4.Arjun takes 40 seconds and Aarav 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?
  5. 5.Three temple bells ring every 24, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 10, 12 or 6.
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 10, 3 or 12.
  9. 9.Two tanks hold 175 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Two tanks hold 80 litres and 70 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 300 cm long and 250 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 8 that leaves a remainder of 3 when divided by 8, 4 or 6.
  13. 13.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?
  14. 14.Zoya takes 36 seconds and Saanvi 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?
  15. 15.Two tanks hold 75 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Two tanks hold 105 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 10.
  18. 18.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?
  19. 19.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Two tanks hold 100 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Tara takes 45 seconds and Aditya 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.Tara takes 90 seconds and Ananya 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?
  23. 23.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 5, 4 or 3.
  24. 24.Three temple bells ring every 10, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 150 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 3.
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 10, 15 or 5.
  28. 28.Three temple bells ring every 12, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 6.
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 4.
  31. 31.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Two tanks hold 25 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Two tanks hold 140 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 8 or 9.
  36. 36.Two tanks hold 400 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Two tanks hold 120 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Saanvi takes 30 seconds and Karan 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?
  39. 39.Farhan takes 90 seconds and Saanvi 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?
  40. 40.Three temple bells ring every 10, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 90
  2. 120
  3. 240
  4. 120
  5. 72
  6. 56
  7. 65
  8. 62
  9. 25
  10. 10
  11. 30
  12. 27
  13. 6
  14. 180
  15. 25
  16. 15
  17. 61
  18. 21
  19. 14
  20. 20
  21. 720
  22. 270
  23. 62
  24. 60
  25. 50
  26. 32
  27. 33
  28. 36
  29. 31
  30. 61
  31. 12
  32. 5
  33. 25
  34. 20
  35. 74
  36. 50
  37. 30
  38. 240
  39. 360
  40. 40

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