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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 402 · 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 12 that leaves a remainder of 3 when divided by 4, 6 or 12.
  2. 2.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 3 or 6.
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 3.
  4. 4.Two tanks hold 225 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Arjun takes 45 seconds and Rahul 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?
  6. 6.Two tanks hold 30 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Kabir takes 45 seconds and Dev 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?
  8. 8.Two tanks hold 20 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Two tanks hold 240 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Two tanks hold 100 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Zoya takes 30 seconds and Karan 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?
  12. 12.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Two tanks hold 300 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.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?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 12, 15 or 5.
  16. 16.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?
  17. 17.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 5 or 3.
  18. 18.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?
  19. 19.Meera takes 54 seconds and Diya 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?
  20. 20.Three temple bells ring every 9, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 4.
  22. 22.Three temple bells ring every 8, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 225 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Aarav takes 48 seconds and Meera 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?
  26. 26.Two tanks hold 45 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 5, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 3 or 6.
  29. 29.Three temple bells ring every 6, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Vivaan takes 75 seconds and Diya 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?
  31. 31.Aarav takes 72 seconds and Diya 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?
  32. 32.Diya takes 40 seconds and Kavya 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?
  33. 33.Two tanks hold 210 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 10.
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 9 or 8.
  36. 36.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Three temple bells ring every 6, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.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?
  39. 39.Three temple bells ring every 5, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 15
  2. 13
  3. 37
  4. 45
  5. 720
  6. 5
  7. 720
  8. 5
  9. 30
  10. 20
  11. 120
  12. 35
  13. 50
  14. 24
  15. 64
  16. 10
  17. 121
  18. 24
  19. 270
  20. 90
  21. 62
  22. 120
  23. 25
  24. 6
  25. 720
  26. 15
  27. 120
  28. 14
  29. 60
  30. 300
  31. 360
  32. 360
  33. 30
  34. 61
  35. 76
  36. 56
  37. 120
  38. 25
  39. 60
  40. 15

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