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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 474 · 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).

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  1. 1.Three temple bells ring every 30, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 12 or 3.
  3. 3.Dev takes 60 seconds and Karan 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?
  4. 4.Two tanks hold 200 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Three temple bells ring every 12, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 4, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.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?
  8. 8.Two tanks hold 60 litres and 70 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 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.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?
  11. 11.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Two tanks hold 270 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Two tanks hold 50 litres and 175 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 10 that leaves a remainder of 2 when divided by 10, 5 or 3.
  15. 15.Three temple bells ring every 6, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Kabir takes 60 seconds and Zoya 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?
  17. 17.Three temple bells ring every 8, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Two tanks hold 250 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Aditya takes 40 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?
  20. 20.Two tanks hold 175 litres and 225 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 4, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 15 or 5.
  24. 24.Saanvi takes 72 seconds and Ananya 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?
  25. 25.Three temple bells ring every 30, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Aditya takes 48 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?
  27. 27.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?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 10, 15 or 6.
  29. 29.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Three temple bells ring every 30, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Arjun takes 60 seconds and Kabir 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?
  32. 32.Kavya takes 45 seconds and Sneha 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?
  33. 33.Dev takes 54 seconds and Meera 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?
  34. 34.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 24, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 8.
  37. 37.Three temple bells ring every 10, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Arjun takes 45 seconds and Rohan 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?
  40. 40.Aarav takes 40 seconds and Pooja 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?

Answer key

  1. 60
  2. 14
  3. 300
  4. 40
  5. 60
  6. 120
  7. 24
  8. 10
  9. 20
  10. 14
  11. 6
  12. 30
  13. 25
  14. 32
  15. 60
  16. 360
  17. 120
  18. 50
  19. 120
  20. 25
  21. 60
  22. 24
  23. 61
  24. 144
  25. 120
  26. 240
  27. 21
  28. 35
  29. 14
  30. 90
  31. 180
  32. 360
  33. 216
  34. 12
  35. 120
  36. 121
  37. 90
  38. 14
  39. 360
  40. 240

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