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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 156 · 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.Three temple bells ring every 15, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 120 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Kavya takes 48 seconds and Arjun 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?
  4. 4.Meera takes 54 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?
  5. 5.Three temple bells ring every 24, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 18, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 50 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Three temple bells ring every 15, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 70 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 12 or 5.
  11. 11.A hall floor is 60 cm long and 40 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 15 that leaves a remainder of 3 when divided by 15, 6 or 4.
  13. 13.Two tanks hold 120 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Two tanks hold 120 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 6 or 15.
  16. 16.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Pooja takes 90 seconds and Karan 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?
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 6 or 10.
  19. 19.Two tanks hold 280 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.Three temple bells ring every 20, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 3 or 8.
  22. 22.Tara takes 50 seconds and Saanvi 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?
  23. 23.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Two tanks hold 40 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 12, 6 or 15.
  27. 27.Two tanks hold 140 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Two tanks hold 125 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Two tanks hold 180 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 9, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 6 or 5.
  32. 32.Two tanks hold 150 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.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?
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 5 when divided by 6, 9 or 10.
  35. 35.Kabir takes 45 seconds and Nisha 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?
  36. 36.Zoya takes 48 seconds and Vivaan 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?
  37. 37.Isha takes 40 seconds and Tara 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?
  38. 38.Sneha takes 50 seconds and Meera 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?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 5.
  40. 40.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?

Answer key

  1. 60
  2. 15
  3. 720
  4. 270
  5. 120
  6. 90
  7. 25
  8. 60
  9. 10
  10. 61
  11. 6
  12. 63
  13. 40
  14. 40
  15. 92
  16. 15
  17. 180
  18. 34
  19. 40
  20. 120
  21. 74
  22. 150
  23. 6
  24. 10
  25. 5
  26. 64
  27. 20
  28. 25
  29. 45
  30. 72
  31. 61
  32. 30
  33. 15
  34. 95
  35. 360
  36. 432
  37. 360
  38. 400
  39. 181
  40. 45

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