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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 44 · 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.Kabir takes 36 seconds and Kavya 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?
  2. 2.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?
  3. 3.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?
  4. 4.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Two tanks hold 20 litres and 50 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 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Two tanks hold 35 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 9 or 3.
  11. 11.Two tanks hold 150 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 3.
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 9 or 6.
  14. 14.A hall floor is 420 cm long and 120 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 6 that leaves a remainder of 2 when divided by 4, 6 or 5.
  16. 16.Two tanks hold 225 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Aarav takes 36 seconds and Karan 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?
  18. 18.Three temple bells ring every 24, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 210 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Kabir takes 80 seconds and Dev 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?
  21. 21.Vivaan takes 48 seconds and Isha 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?
  22. 22.Diya takes 30 seconds and Zoya 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?
  23. 23.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 3 or 4.
  24. 24.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 5, 4 or 6.
  25. 25.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 9 or 5.
  26. 26.Two tanks hold 350 litres and 250 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 10, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 10, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 150 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 6.
  31. 31.Rohan takes 60 seconds and Sneha 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?
  32. 32.Three temple bells ring every 5, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 25 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Three temple bells ring every 20, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 8 or 4.
  36. 36.Meera takes 80 seconds and Aditya 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?
  37. 37.Aditya takes 45 seconds and Farhan 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?
  38. 38.Arjun takes 40 seconds and Rahul 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?
  39. 39.Aditya takes 72 seconds and Priya 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?
  40. 40.Two tanks hold 100 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 144
  2. 6
  3. 14
  4. 42
  5. 10
  6. 42
  7. 6
  8. 5
  9. 12
  10. 91
  11. 30
  12. 32
  13. 37
  14. 14
  15. 62
  16. 45
  17. 180
  18. 120
  19. 30
  20. 720
  21. 240
  22. 240
  23. 25
  24. 61
  25. 181
  26. 50
  27. 20
  28. 120
  29. 50
  30. 13
  31. 180
  32. 60
  33. 5
  34. 60
  35. 122
  36. 240
  37. 90
  38. 600
  39. 360
  40. 20

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