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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 473 · 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.Saanvi takes 80 seconds and Diya 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?
  2. 2.Saanvi takes 36 seconds and Rohan 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?
  3. 3.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 6.
  4. 4.Three temple bells ring every 6, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 4 or 6.
  6. 6.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Nisha takes 30 seconds and Sneha 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?
  8. 8.Isha takes 45 seconds and Ishaan 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?
  9. 9.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 8 or 10.
  10. 10.Two tanks hold 360 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 5.
  12. 12.Two tanks hold 50 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 3 or 15.
  14. 14.Three temple bells ring every 10, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Two tanks hold 15 litres and 35 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 4, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.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?
  18. 18.Three temple bells ring every 30, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 100 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Two tanks hold 200 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Two tanks hold 225 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 9 or 10.
  23. 23.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 5 or 9.
  24. 24.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Aditya takes 75 seconds and Kabir 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?
  26. 26.Three temple bells ring every 24, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Sneha takes 90 seconds and Kavya 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?
  28. 28.Two tanks hold 45 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Three temple bells ring every 30, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Diya takes 45 seconds and Zoya 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?
  31. 31.Three temple bells ring every 15, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.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?
  33. 33.Three temple bells ring every 6, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Ananya takes 80 seconds and Isha 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?
  36. 36.Farhan takes 48 seconds and Nisha 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?
  37. 37.Three temple bells ring every 10, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 3.
  39. 39.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?
  40. 40.Three temple bells ring every 8, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 240
  2. 720
  3. 20
  4. 120
  5. 61
  6. 42
  7. 150
  8. 360
  9. 43
  10. 40
  11. 31
  12. 10
  13. 46
  14. 60
  15. 5
  16. 120
  17. 40
  18. 120
  19. 20
  20. 50
  21. 25
  22. 181
  23. 47
  24. 15
  25. 150
  26. 120
  27. 180
  28. 15
  29. 60
  30. 180
  31. 120
  32. 56
  33. 120
  34. 15
  35. 720
  36. 720
  37. 90
  38. 61
  39. 24
  40. 120

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