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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 397 · 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.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 6 or 4.
  2. 2.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 8.
  3. 3.Three temple bells ring every 6, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 225 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Two tanks hold 20 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Arjun takes 60 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?
  7. 7.Three temple bells ring every 5, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 10 or 15.
  9. 9.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 8 or 10.
  10. 10.Isha takes 45 seconds and Vivaan 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?
  11. 11.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.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?
  13. 13.Three temple bells ring every 4, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.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?
  15. 15.Two tanks hold 40 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 12, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Dev takes 36 seconds and Meera 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?
  18. 18.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 4 or 3.
  20. 20.Two tanks hold 10 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 30, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.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?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 4.
  24. 24.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?
  25. 25.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 4, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Diya takes 50 seconds and Zoya 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?
  28. 28.Karan takes 60 seconds and Manav 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?
  29. 29.Three temple bells ring every 10, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Meera takes 60 seconds and Pooja 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?
  31. 31.Three temple bells ring every 6, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 60 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Saanvi takes 80 seconds and Vivaan 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?
  34. 34.Sneha takes 48 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?
  35. 35.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Three temple bells ring every 8, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.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?
  38. 38.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 6.
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 8 or 12.
  40. 40.Three temple bells ring every 24, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 62
  2. 122
  3. 60
  4. 45
  5. 5
  6. 300
  7. 60
  8. 91
  9. 121
  10. 360
  11. 28
  12. 35
  13. 72
  14. 56
  15. 10
  16. 60
  17. 360
  18. 24
  19. 26
  20. 5
  21. 120
  22. 20
  23. 62
  24. 24
  25. 56
  26. 60
  27. 200
  28. 240
  29. 120
  30. 540
  31. 90
  32. 15
  33. 720
  34. 720
  35. 14
  36. 120
  37. 40
  38. 31
  39. 26
  40. 72

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