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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 485 · 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, 9 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.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?
  3. 3.Three temple bells ring every 24, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 4 or 9.
  5. 5.Three temple bells ring every 4, 6 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 2 when divided by 3, 4 or 10.
  7. 7.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 8 or 9.
  8. 8.Tara takes 72 seconds and Karan 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?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 9 or 6.
  10. 10.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Three temple bells ring every 24, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 10 or 15.
  13. 13.Three temple bells ring every 15, 6 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 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.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?
  16. 16.Two tanks hold 210 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 10, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Diya takes 80 seconds and Ananya 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?
  19. 19.Ananya takes 75 seconds and Rahul 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?
  20. 20.Diya takes 80 seconds and Rohan 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?
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 4.
  22. 22.Three temple bells ring every 10, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.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?
  24. 24.Two tanks hold 350 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.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?
  27. 27.Priya takes 48 seconds and Saanvi 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.Three temple bells ring every 6, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 20, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 24, 20 and 12 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 6 that leaves a remainder of 2 when divided by 3, 4 or 6.
  32. 32.Two tanks hold 200 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Pooja takes 30 seconds and Saanvi 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?
  35. 35.Isha takes 36 seconds and Arjun 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?
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 5.
  37. 37.Three temple bells ring every 15, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Kavya takes 30 seconds and Meera 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?
  39. 39.Two tanks hold 100 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 5, 12 or 9.

Answer key

  1. 36
  2. 30
  3. 120
  4. 73
  5. 60
  6. 62
  7. 73
  8. 360
  9. 95
  10. 12
  11. 72
  12. 63
  13. 60
  14. 120
  15. 56
  16. 30
  17. 30
  18. 240
  19. 150
  20. 720
  21. 61
  22. 60
  23. 12
  24. 50
  25. 40
  26. 6
  27. 432
  28. 30
  29. 120
  30. 120
  31. 14
  32. 40
  33. 14
  34. 240
  35. 144
  36. 17
  37. 120
  38. 240
  39. 50
  40. 184

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