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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 348 · 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 20, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 6.
  3. 3.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 10, 8 or 5.
  4. 4.Two tanks hold 120 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Three temple bells ring every 4, 8 and 6 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, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Diya takes 80 seconds and Dev 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?
  10. 10.Kabir takes 40 seconds and Farhan 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?
  11. 11.Two tanks hold 100 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Ananya takes 45 seconds and Priya 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?
  13. 13.Three temple bells ring every 5, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 5, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Isha takes 48 seconds and Ananya 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?
  16. 16.Three temple bells ring every 24, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Vivaan takes 30 seconds and Aarav 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?
  18. 18.Saanvi takes 40 seconds and Pooja 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?
  19. 19.Three temple bells ring every 4, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Two tanks hold 200 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Diya takes 48 seconds and Aarav 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?
  22. 22.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 8 or 6.
  23. 23.Three temple bells ring every 8, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 9, 4 or 10.
  25. 25.Rohan takes 30 seconds and Kavya 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?
  26. 26.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 4 or 3.
  27. 27.Pooja takes 60 seconds and Karan takes 72 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.Three temple bells ring every 4, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 120 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Ananya takes 45 seconds and Ishaan 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?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 9 or 15.
  32. 32.Ananya takes 30 seconds and Diya 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?
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 3 or 15.
  34. 34.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?
  35. 35.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?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 7 when divided by 9, 12 or 10.
  37. 37.Meera takes 48 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?
  38. 38.Meera takes 50 seconds and Diya 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?
  39. 39.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 6 or 4.
  40. 40.Three temple bells ring every 15, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 60
  2. 32
  3. 44
  4. 15
  5. 35
  6. 40
  7. 24
  8. 120
  9. 720
  10. 120
  11. 50
  12. 720
  13. 60
  14. 120
  15. 240
  16. 120
  17. 90
  18. 240
  19. 40
  20. 50
  21. 240
  22. 26
  23. 120
  24. 182
  25. 240
  26. 13
  27. 360
  28. 20
  29. 30
  30. 450
  31. 182
  32. 90
  33. 16
  34. 10
  35. 15
  36. 187
  37. 240
  38. 300
  39. 39
  40. 60

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