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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 118 · 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).

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  1. 1.Two tanks hold 120 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 8 or 10.
  3. 3.Ishaan takes 75 seconds and Arjun 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?
  4. 4.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Three temple bells ring every 24, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 9, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 4.
  8. 8.Meera takes 90 seconds and Sneha 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?
  9. 9.Two tanks hold 360 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Three temple bells ring every 6, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 250 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 12, 5 or 15.
  13. 13.Three temple bells ring every 24, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 5, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Dev takes 54 seconds and Ishaan 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?
  16. 16.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 10 or 6.
  17. 17.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Three temple bells ring every 8, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 250 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Three temple bells ring every 9, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Two tanks hold 105 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Two tanks hold 125 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 3 or 5.
  24. 24.A hall floor is 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.A hall floor is 200 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 5, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.A hall floor is 225 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Saanvi takes 40 seconds and Aarav 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?
  29. 29.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Two tanks hold 200 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 6, 18 and 10 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 4 when divided by 12, 6 or 10.
  33. 33.Three temple bells ring every 12, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 15 or 10.
  35. 35.Three temple bells ring every 30, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 5, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Karan takes 72 seconds and Tara 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?
  39. 39.Meera takes 48 seconds and Manav 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?
  40. 40.Three temple bells ring every 8, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 15
  2. 42
  3. 150
  4. 15
  5. 120
  6. 90
  7. 37
  8. 720
  9. 40
  10. 36
  11. 50
  12. 64
  13. 120
  14. 90
  15. 432
  16. 32
  17. 21
  18. 120
  19. 50
  20. 36
  21. 15
  22. 25
  23. 31
  24. 56
  25. 15
  26. 60
  27. 20
  28. 360
  29. 25
  30. 40
  31. 90
  32. 64
  33. 60
  34. 61
  35. 60
  36. 120
  37. 28
  38. 360
  39. 240
  40. 120

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