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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 120 · 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.Dev takes 90 seconds and Farhan 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?
  2. 2.Three temple bells ring every 4, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 6 when divided by 12, 10 or 8.
  4. 4.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 5.
  6. 6.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 12 or 4.
  7. 7.Two tanks hold 60 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 9.
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 12 or 3.
  10. 10.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Two tanks hold 25 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Aarav takes 36 seconds and Rahul 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?
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 10 or 8.
  14. 14.A hall floor is 480 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Two tanks hold 90 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Three temple bells ring every 8, 18 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 30, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Two tanks hold 60 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 15 or 12.
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 3 or 10.
  21. 21.Three temple bells ring every 4, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 4 or 3.
  23. 23.Three temple bells ring every 24, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Aarav takes 40 seconds and Ananya 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?
  25. 25.Two tanks hold 360 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Three temple bells ring every 6, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 50 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.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?
  29. 29.Zoya 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?
  30. 30.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 8 or 3.
  31. 31.Two tanks hold 360 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Zoya takes 36 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.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?
  34. 34.A hall floor is 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Saanvi takes 60 seconds and Manav 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?
  36. 36.Ishaan takes 45 seconds and Rahul 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?
  37. 37.Three temple bells ring every 15, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.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?
  40. 40.Two tanks hold 50 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 180
  2. 72
  3. 126
  4. 42
  5. 181
  6. 62
  7. 20
  8. 182
  9. 14
  10. 21
  11. 5
  12. 180
  13. 43
  14. 40
  15. 10
  16. 72
  17. 90
  18. 15
  19. 61
  20. 121
  21. 60
  22. 25
  23. 120
  24. 360
  25. 45
  26. 24
  27. 10
  28. 90
  29. 240
  30. 73
  31. 40
  32. 360
  33. 14
  34. 24
  35. 300
  36. 90
  37. 60
  38. 24
  39. 10
  40. 10

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