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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 150 · 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 4, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 3.
  3. 3.Rohan takes 80 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?
  4. 4.Two tanks hold 225 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Three temple bells ring every 18, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 5 when divided by 6, 10 or 8.
  7. 7.Arjun takes 30 seconds and Rohan 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?
  8. 8.Three temple bells ring every 8, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Rohan takes 54 seconds and Diya 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?
  10. 10.Three temple bells ring every 15, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Meera takes 80 seconds and Aditya 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?
  12. 12.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?
  13. 13.A hall floor is 270 cm long and 225 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 4, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 30, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.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?
  18. 18.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 6, 12 or 9.
  19. 19.Three temple bells ring every 6, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Two tanks hold 120 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.Three temple bells ring every 5, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 9, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 135 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Isha takes 30 seconds and Diya 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?
  25. 25.A hall floor is 210 cm long and 120 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 30, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 25 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Saanvi takes 90 seconds and Arjun takes 40 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?
  29. 29.Three temple bells ring every 30, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.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?
  31. 31.Find the smallest number bigger than 9 that leaves a remainder of 4 when divided by 5, 9 or 6.
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 8 or 4.
  33. 33.Two tanks hold 200 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Three temple bells ring every 10, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Three temple bells ring every 12, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 3 or 10.
  38. 38.Kavya takes 90 seconds and Vivaan 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?
  39. 39.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 5, 6 or 3.

Answer key

  1. 60
  2. 31
  3. 720
  4. 45
  5. 90
  6. 125
  7. 150
  8. 72
  9. 270
  10. 30
  11. 240
  12. 10
  13. 30
  14. 60
  15. 120
  16. 6
  17. 24
  18. 39
  19. 60
  20. 40
  21. 60
  22. 90
  23. 45
  24. 270
  25. 28
  26. 90
  27. 5
  28. 360
  29. 120
  30. 120
  31. 94
  32. 121
  33. 25
  34. 20
  35. 56
  36. 60
  37. 31
  38. 450
  39. 12
  40. 31

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