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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 534 · 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.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?
  2. 2.Diya takes 90 seconds and Saanvi 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?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 9.
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 5 or 15.
  5. 5.Vivaan takes 75 seconds and Kavya 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?
  6. 6.Dev takes 30 seconds and Diya 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?
  7. 7.Three temple bells ring every 10, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 24, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 10 or 3.
  10. 10.Two tanks hold 105 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Karan takes 75 seconds and Nisha 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?
  13. 13.Two tanks hold 30 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Isha takes 48 seconds and Nisha 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?
  15. 15.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Tara takes 40 seconds and Karan 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?
  17. 17.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Two tanks hold 280 litres and 160 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 2 when divided by 15, 5 or 12.
  20. 20.Three temple bells ring every 30, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Two tanks hold 150 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Three temple bells ring every 18, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Three temple bells ring every 20, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 10, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.A hall floor is 400 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Two tanks hold 50 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 150 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.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?
  31. 31.Two tanks hold 75 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 10 or 9.
  33. 33.Three temple bells ring every 4, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Kavya takes 80 seconds and Vivaan 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?
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 5.
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 12, 15 or 10.
  37. 37.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 6, 5 or 8.
  38. 38.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?
  39. 39.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 6, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 40
  2. 450
  3. 37
  4. 122
  5. 300
  6. 120
  7. 60
  8. 120
  9. 32
  10. 15
  11. 21
  12. 225
  13. 10
  14. 144
  15. 30
  16. 240
  17. 14
  18. 40
  19. 62
  20. 120
  21. 25
  22. 90
  23. 56
  24. 120
  25. 40
  26. 40
  27. 12
  28. 25
  29. 50
  30. 24
  31. 25
  32. 95
  33. 120
  34. 400
  35. 61
  36. 64
  37. 123
  38. 10
  39. 15
  40. 90

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