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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 400 · 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 2 when divided by 3, 6 or 8.
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 15 or 9.
  3. 3.Sneha takes 36 seconds and Aarav 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.A hall floor is 175 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Two tanks hold 75 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Zoya takes 72 seconds and Farhan 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?
  8. 8.Three temple bells ring every 30, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.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?
  10. 10.Three temple bells ring every 8, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 75 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.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?
  13. 13.Two tanks hold 30 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 4 or 15.
  15. 15.Saanvi takes 75 seconds and Nisha 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?
  16. 16.Two tanks hold 250 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.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?
  18. 18.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 5.
  19. 19.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.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?
  22. 22.Two tanks hold 30 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Ishaan takes 50 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?
  24. 24.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 3 or 5.
  25. 25.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 9, 12 or 3.
  26. 26.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 3 or 9.
  27. 27.Two tanks hold 150 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Diya takes 90 seconds and Dev 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?
  29. 29.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 8.
  30. 30.Saanvi takes 45 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?
  31. 31.Two tanks hold 100 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 3 or 10.
  33. 33.Vivaan takes 50 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?
  34. 34.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.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?
  36. 36.Dev takes 30 seconds and Saanvi 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?
  37. 37.Two tanks hold 15 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Two tanks hold 60 litres and 105 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 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 26
  2. 92
  3. 180
  4. 28
  5. 14
  6. 15
  7. 360
  8. 60
  9. 24
  10. 40
  11. 15
  12. 30
  13. 5
  14. 61
  15. 150
  16. 50
  17. 35
  18. 61
  19. 20
  20. 21
  21. 50
  22. 10
  23. 300
  24. 121
  25. 38
  26. 19
  27. 30
  28. 180
  29. 121
  30. 90
  31. 25
  32. 91
  33. 400
  34. 14
  35. 24
  36. 240
  37. 5
  38. 24
  39. 15
  40. 10

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