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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 427 · 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 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 5.
  3. 3.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?
  4. 4.Rahul takes 45 seconds and Arjun 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?
  5. 5.A hall floor is 200 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Three temple bells ring every 12, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.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?
  8. 8.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?
  9. 9.Two tanks hold 100 litres and 225 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 10, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 6, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 6, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  14. 14.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 6, 12 or 9.
  16. 16.Two tanks hold 105 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 4, 5 or 3.
  18. 18.Three temple bells ring every 6, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 90 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Kavya takes 40 seconds and Meera 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?
  21. 21.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Isha takes 40 seconds and Kabir 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?
  23. 23.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 8, 4 or 5.
  24. 24.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 10 or 8.
  25. 25.Ananya takes 80 seconds and Aarav 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?
  26. 26.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Three temple bells ring every 6, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 350 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Ananya takes 50 seconds and Saanvi 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?
  30. 30.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?
  31. 31.Three temple bells ring every 12, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 24, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.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?
  34. 34.Three temple bells ring every 4, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Two tanks hold 150 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 8.
  38. 38.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 9.
  40. 40.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 42
  2. 62
  3. 6
  4. 450
  5. 40
  6. 24
  7. 28
  8. 28
  9. 25
  10. 90
  11. 36
  12. 120
  13. 31
  14. 14
  15. 41
  16. 15
  17. 62
  18. 30
  19. 30
  20. 360
  21. 21
  22. 240
  23. 43
  24. 42
  25. 240
  26. 21
  27. 60
  28. 50
  29. 150
  30. 15
  31. 120
  32. 120
  33. 30
  34. 36
  35. 14
  36. 30
  37. 121
  38. 14
  39. 182
  40. 20

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