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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 302 · 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.Isha takes 60 seconds and Zoya 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?
  2. 2.Three temple bells ring every 5, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 8, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 8, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.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?
  6. 6.Two tanks hold 450 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 9, 12 or 10.
  8. 8.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 4 or 6.
  9. 9.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 8 or 4.
  10. 10.Three temple bells ring every 18, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 4 or 10.
  13. 13.Three temple bells ring every 10, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Two tanks hold 120 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Two tanks hold 180 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 30, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 3 or 5.
  20. 20.Three temple bells ring every 6, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Aarav takes 36 seconds and Karan takes 90 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.Two tanks hold 70 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 8.
  24. 24.Two tanks hold 100 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Nisha takes 30 seconds and Arjun 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?
  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.Rahul takes 72 seconds and Kabir 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?
  29. 29.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Three temple bells ring every 15, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.A hall floor is 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Three temple bells ring every 20, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 4, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 15, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 15 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 6, 10 or 15.
  39. 39.Two tanks hold 180 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Three temple bells ring every 8, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 300
  2. 120
  3. 120
  4. 120
  5. 24
  6. 50
  7. 183
  8. 62
  9. 41
  10. 72
  11. 20
  12. 181
  13. 60
  14. 30
  15. 10
  16. 40
  17. 30
  18. 60
  19. 47
  20. 90
  21. 180
  22. 10
  23. 121
  24. 50
  25. 56
  26. 270
  27. 20
  28. 720
  29. 21
  30. 35
  31. 60
  32. 40
  33. 60
  34. 120
  35. 90
  36. 5
  37. 10
  38. 34
  39. 45
  40. 120

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