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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 374 · 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.Nisha takes 36 seconds and Tara 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?
  2. 2.Dev takes 30 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?
  3. 3.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 10 or 9.
  4. 4.Three temple bells ring every 8, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 3.
  6. 6.Three temple bells ring every 15, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Kavya takes 72 seconds and Rahul 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?
  8. 8.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 10 or 3.
  9. 9.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Two tanks hold 180 litres and 210 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 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Three temple bells ring every 10, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Three temple bells ring every 20, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 20, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 3 or 15.
  16. 16.Three temple bells ring every 15, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 6, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Two tanks hold 45 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.Saanvi takes 36 seconds and Aditya takes 45 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.Two tanks hold 60 litres and 70 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 20, 4 and 24 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, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Three temple bells ring every 15, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Diya takes 60 seconds and Ananya 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?
  26. 26.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?
  27. 27.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 9, 10 or 3.
  28. 28.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?
  29. 29.Farhan takes 45 seconds and Kavya 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?
  30. 30.Two tanks hold 70 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 9.
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 4.
  33. 33.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 4.
  34. 34.A hall floor is 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 18, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Saanvi takes 40 seconds and Farhan 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?
  37. 37.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?
  38. 38.Aditya takes 50 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?
  39. 39.Dev takes 30 seconds and Tara 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?
  40. 40.Rohan takes 36 seconds and Saanvi 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?

Answer key

  1. 360
  2. 240
  3. 182
  4. 72
  5. 62
  6. 120
  7. 360
  8. 121
  9. 15
  10. 30
  11. 56
  12. 90
  13. 60
  14. 60
  15. 62
  16. 90
  17. 30
  18. 15
  19. 180
  20. 10
  21. 120
  22. 90
  23. 12
  24. 60
  25. 300
  26. 6
  27. 92
  28. 6
  29. 180
  30. 10
  31. 91
  32. 61
  33. 37
  34. 40
  35. 90
  36. 360
  37. 50
  38. 300
  39. 270
  40. 180

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