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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 19 · 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.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 3 or 15.
  2. 2.Two tanks hold 75 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 9 or 12.
  4. 4.Arjun takes 36 seconds and Zoya 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?
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 6, 15 or 9.
  6. 6.Three temple bells ring every 12, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 6, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 3 or 8.
  9. 9.Tara takes 54 seconds and Arjun 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?
  10. 10.Three temple bells ring every 20, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 8, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Kavya takes 54 seconds and Zoya 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?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 9.
  14. 14.Two tanks hold 30 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 30, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 4, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Aarav takes 54 seconds and Saanvi 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?
  18. 18.Rahul takes 80 seconds and Karan 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?
  19. 19.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?
  20. 20.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Three temple bells ring every 8, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 6 or 9.
  23. 23.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?
  24. 24.Two tanks hold 280 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 20, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 6, 8 or 3.
  27. 27.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Three temple bells ring every 30, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Sneha takes 45 seconds and Rohan 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?
  30. 30.Two tanks hold 35 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Two tanks hold 270 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.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?
  33. 33.Meera takes 50 seconds and Ananya 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?
  34. 34.Kabir takes 40 seconds and Rahul 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?
  35. 35.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?
  36. 36.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 5.
  37. 37.Three temple bells ring every 8, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Two tanks hold 35 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.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?
  40. 40.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 6, 12 or 8.

Answer key

  1. 62
  2. 25
  3. 39
  4. 180
  5. 93
  6. 36
  7. 60
  8. 25
  9. 270
  10. 120
  11. 72
  12. 270
  13. 182
  14. 15
  15. 60
  16. 60
  17. 270
  18. 720
  19. 30
  20. 28
  21. 120
  22. 19
  23. 25
  24. 40
  25. 60
  26. 26
  27. 10
  28. 60
  29. 360
  30. 5
  31. 30
  32. 60
  33. 200
  34. 360
  35. 24
  36. 122
  37. 72
  38. 5
  39. 56
  40. 26

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