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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 183 · 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.Saanvi takes 50 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?
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 10, 6 or 15.
  3. 3.Arjun takes 60 seconds and Isha 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?
  4. 4.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 5, 4 or 8.
  5. 5.Three temple bells ring every 20, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.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?
  7. 7.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?
  8. 8.Priya takes 48 seconds and Manav 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?
  9. 9.Two tanks hold 175 litres and 225 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 150 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 6.
  12. 12.Two tanks hold 40 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.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?
  14. 14.Three temple bells ring every 30, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Two tanks hold 300 litres and 350 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 120 litres and 100 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 9 that leaves a remainder of 2 when divided by 9, 4 or 8.
  18. 18.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 10, 12 or 15.
  20. 20.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 5 or 12.
  21. 21.Two tanks hold 50 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.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?
  23. 23.Three temple bells ring every 20, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 8, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 6 or 4.
  26. 26.Rohan takes 90 seconds and Karan takes 75 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.Ananya takes 72 seconds and Meera 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?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 6 or 12.
  29. 29.Two tanks hold 60 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Aditya takes 36 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?
  31. 31.Aditya takes 90 seconds and Rohan 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?
  32. 32.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 3 or 12.
  34. 34.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?
  35. 35.Two tanks hold 80 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 8, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 50 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 10.
  39. 39.Three temple bells ring every 10, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 18, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 400
  2. 35
  3. 180
  4. 43
  5. 60
  6. 5
  7. 20
  8. 240
  9. 25
  10. 30
  11. 31
  12. 20
  13. 24
  14. 120
  15. 50
  16. 20
  17. 74
  18. 30
  19. 65
  20. 61
  21. 10
  22. 50
  23. 40
  24. 120
  25. 13
  26. 450
  27. 216
  28. 13
  29. 30
  30. 108
  31. 720
  32. 24
  33. 37
  34. 24
  35. 10
  36. 120
  37. 10
  38. 61
  39. 60
  40. 72

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