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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 448 · 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.Two tanks hold 160 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Diya takes 54 seconds and Nisha 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?
  4. 4.Ananya takes 40 seconds and Saanvi 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?
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 4 or 15.
  6. 6.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?
  7. 7.Farhan takes 72 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?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 12 or 5.
  9. 9.Sneha takes 40 seconds and Aditya 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?
  10. 10.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?
  11. 11.Three temple bells ring every 4, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 5 or 8.
  13. 13.Two tanks hold 100 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Three temple bells ring every 15, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 4, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Isha takes 75 seconds and Kavya 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?
  17. 17.Three temple bells ring every 4, 5 and 24 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 9 that leaves a remainder of 1 when divided by 4, 9 or 5.
  19. 19.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?
  20. 20.Two tanks hold 450 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 20, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Two tanks hold 350 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 4, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Nisha takes 75 seconds and Meera 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?
  26. 26.Ananya takes 45 seconds and Pooja 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?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 6, 12 or 15.
  28. 28.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?
  29. 29.Two tanks hold 90 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 8, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 8, 4 or 5.
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 10 or 15.
  34. 34.Meera takes 90 seconds and Diya 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?
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 10.
  36. 36.Three temple bells ring every 8, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 5, 9 or 10.
  38. 38.Two tanks hold 40 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Kabir takes 80 seconds and Isha 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?
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 9, 12 or 15.

Answer key

  1. 20
  2. 12
  3. 270
  4. 120
  5. 62
  6. 21
  7. 360
  8. 62
  9. 240
  10. 28
  11. 40
  12. 122
  13. 50
  14. 45
  15. 72
  16. 150
  17. 120
  18. 181
  19. 6
  20. 50
  21. 60
  22. 6
  23. 50
  24. 60
  25. 600
  26. 360
  27. 64
  28. 50
  29. 10
  30. 40
  31. 35
  32. 43
  33. 31
  34. 180
  35. 61
  36. 120
  37. 93
  38. 10
  39. 240
  40. 185

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