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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 73 · 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 8 that leaves a remainder of 1 when divided by 6, 8 or 5.
  2. 2.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 4.
  4. 4.Two tanks hold 200 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Two tanks hold 120 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.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?
  7. 7.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 8.
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 10 or 12.
  10. 10.Kabir takes 80 seconds and Karan 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?
  11. 11.A hall floor is 180 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Pooja takes 60 seconds and Kavya 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?
  13. 13.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 5 or 9.
  14. 14.Nisha takes 80 seconds and Isha 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?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 15 or 5.
  16. 16.Pooja takes 75 seconds and Ananya 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?
  17. 17.Three temple bells ring every 4, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Two tanks hold 80 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Three temple bells ring every 8, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Ananya takes 80 seconds and Priya 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?
  21. 21.Find the smallest number bigger than 12 that leaves a remainder of 6 when divided by 8, 9 or 12.
  22. 22.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 9.
  23. 23.Isha takes 30 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?
  24. 24.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?
  25. 25.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?
  26. 26.Ananya takes 45 seconds and Pooja 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?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 4.
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 12, 9 or 15.
  29. 29.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 6 or 8.
  30. 30.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Three temple bells ring every 8, 12 and 4 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, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.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?
  34. 34.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 30, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 4 or 5.
  37. 37.Arjun takes 40 seconds and Vivaan 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?
  38. 38.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Two tanks hold 360 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.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?

Answer key

  1. 121
  2. 35
  3. 122
  4. 40
  5. 30
  6. 14
  7. 42
  8. 74
  9. 65
  10. 240
  11. 30
  12. 180
  13. 182
  14. 240
  15. 62
  16. 300
  17. 24
  18. 10
  19. 120
  20. 240
  21. 78
  22. 38
  23. 240
  24. 25
  25. 14
  26. 720
  27. 13
  28. 185
  29. 25
  30. 24
  31. 24
  32. 72
  33. 25
  34. 10
  35. 90
  36. 62
  37. 360
  38. 24
  39. 40
  40. 40

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