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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 309 · 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.Rahul takes 75 seconds and Ishaan 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?
  2. 2.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Ananya takes 40 seconds and Isha 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?
  4. 4.Two tanks hold 250 litres and 300 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 270 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Two tanks hold 150 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Three temple bells ring every 6, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.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?
  10. 10.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?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 9 or 15.
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 6 when divided by 12, 8 or 9.
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 3.
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 8, 12 or 9.
  15. 15.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Aarav takes 50 seconds and Isha 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?
  18. 18.Three temple bells ring every 9, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 420 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Vivaan takes 72 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?
  21. 21.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?
  22. 22.Aarav takes 40 seconds and Ananya 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?
  23. 23.Two tanks hold 100 litres and 60 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 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Three temple bells ring every 6, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Pooja takes 30 seconds and Zoya 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?
  27. 27.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 10, 12 or 4.
  29. 29.Three temple bells ring every 9, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Rohan takes 72 seconds and Karan 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.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Two tanks hold 30 litres and 40 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 6 that leaves a remainder of 1 when divided by 4, 5 or 6.
  35. 35.Two tanks hold 225 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 8, 6 or 9.
  37. 37.Rahul takes 40 seconds and Saanvi 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?
  38. 38.Farhan takes 45 seconds and Pooja takes 54 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.Two tanks hold 200 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 8 or 9.

Answer key

  1. 150
  2. 40
  3. 600
  4. 50
  5. 30
  6. 50
  7. 60
  8. 40
  9. 30
  10. 72
  11. 47
  12. 78
  13. 61
  14. 76
  15. 6
  16. 24
  17. 400
  18. 36
  19. 28
  20. 144
  21. 14
  22. 600
  23. 20
  24. 28
  25. 60
  26. 90
  27. 20
  28. 62
  29. 36
  30. 12
  31. 144
  32. 21
  33. 10
  34. 61
  35. 45
  36. 75
  37. 360
  38. 270
  39. 40
  40. 74

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