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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 226 · 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.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?
  2. 2.Three temple bells ring every 15, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 4.
  4. 4.Two tanks hold 210 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 3, 4 or 5.
  6. 6.Rahul takes 50 seconds and Isha 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?
  7. 7.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Two tanks hold 200 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 3.
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 12.
  11. 11.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?
  12. 12.Three temple bells ring every 6, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Three temple bells ring every 4, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 10, 15 or 9.
  15. 15.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 9.
  17. 17.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 6, 10 or 5.
  18. 18.Three temple bells ring every 24, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.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?
  20. 20.Dev takes 60 seconds and Isha 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?
  21. 21.Two tanks hold 180 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Rohan takes 30 seconds and Arjun 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?
  23. 23.Kabir takes 30 seconds and Manav 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?
  24. 24.Two tanks hold 320 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Meera takes 48 seconds and Nisha 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?
  26. 26.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?
  27. 27.Three temple bells ring every 12, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.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?
  29. 29.Three temple bells ring every 10, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Karan takes 48 seconds and Sneha 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?
  31. 31.Three temple bells ring every 15, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 10.
  33. 33.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?
  34. 34.Arjun takes 40 seconds and Saanvi 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?
  35. 35.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 4 or 3.
  36. 36.Two tanks hold 150 litres and 200 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 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?
  38. 38.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 9 or 10.
  39. 39.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?
  40. 40.Three temple bells ring every 10, 15 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 15
  2. 120
  3. 61
  4. 30
  5. 61
  6. 400
  7. 6
  8. 40
  9. 31
  10. 62
  11. 56
  12. 90
  13. 36
  14. 97
  15. 24
  16. 38
  17. 34
  18. 120
  19. 40
  20. 300
  21. 45
  22. 360
  23. 90
  24. 40
  25. 144
  26. 120
  27. 60
  28. 6
  29. 120
  30. 144
  31. 90
  32. 61
  33. 10
  34. 600
  35. 13
  36. 50
  37. 10
  38. 91
  39. 120
  40. 90

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