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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 56 · 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.A hall floor is 420 cm long and 300 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 5, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Two tanks hold 90 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 5 or 10.
  5. 5.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 12 or 3.
  7. 7.Three temple bells ring every 30, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 10, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 10, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 30 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Two tanks hold 30 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 105 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 10, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Ishaan takes 72 seconds and Nisha 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?
  15. 15.Two tanks hold 160 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Two tanks hold 120 litres and 210 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 9, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 8 or 15.
  19. 19.Three temple bells ring every 15, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 20, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Two tanks hold 280 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Three temple bells ring every 8, 15 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 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Vivaan takes 50 seconds and Karan 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?
  25. 25.Saanvi takes 40 seconds and Sneha 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?
  26. 26.Three temple bells ring every 24, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 30, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 18, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.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?
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 6 or 3.
  31. 31.Kavya takes 60 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?
  32. 32.Three temple bells ring every 12, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 75 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Two tanks hold 125 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Kabir takes 90 seconds and Rohan 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?
  36. 36.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 3 or 9.
  37. 37.Zoya takes 30 seconds and Meera 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?
  38. 38.Three temple bells ring every 4, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 15, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 35
  2. 90
  3. 10
  4. 21
  5. 14
  6. 13
  7. 120
  8. 120
  9. 120
  10. 5
  11. 10
  12. 15
  13. 60
  14. 144
  15. 40
  16. 30
  17. 72
  18. 121
  19. 120
  20. 60
  21. 40
  22. 120
  23. 21
  24. 450
  25. 120
  26. 120
  27. 60
  28. 90
  29. 50
  30. 32
  31. 240
  32. 60
  33. 25
  34. 25
  35. 360
  36. 73
  37. 150
  38. 60
  39. 28
  40. 60

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