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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 414 · 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 15 that leaves a remainder of 4 when divided by 9, 15 or 6.
  2. 2.Two tanks hold 80 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Dev takes 90 seconds and Priya 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?
  4. 4.Saanvi takes 50 seconds and Vivaan 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?
  5. 5.Three temple bells ring every 30, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 5 when divided by 6, 10 or 8.
  7. 7.Three temple bells ring every 4, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Dev takes 36 seconds and Zoya 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?
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 9.
  10. 10.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Tara takes 60 seconds and Kabir 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?
  12. 12.Two tanks hold 300 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 24, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Vivaan takes 60 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?
  15. 15.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Two tanks hold 250 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Ishaan takes 40 seconds and Aditya 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?
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 6 or 15.
  19. 19.Nisha takes 72 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?
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 5.
  21. 21.Two tanks hold 45 litres and 75 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 15 that leaves a remainder of 1 when divided by 4, 15 or 5.
  23. 23.Kabir takes 36 seconds and Manav 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?
  24. 24.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Arjun takes 36 seconds and Karan 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?
  26. 26.Three temple bells ring every 12, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Zoya takes 45 seconds and Aarav 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.Three temple bells ring every 6, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Saanvi 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?
  30. 30.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 4 or 6.
  31. 31.Three temple bells ring every 4, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 35 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 18, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Two tanks hold 60 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 5 or 6.
  37. 37.A hall floor is 300 cm long and 120 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 12 that leaves a remainder of 1 when divided by 6, 3 or 12.
  39. 39.Two tanks hold 45 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Two tanks hold 45 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 94
  2. 10
  3. 360
  4. 150
  5. 90
  6. 125
  7. 60
  8. 108
  9. 37
  10. 21
  11. 360
  12. 50
  13. 120
  14. 180
  15. 6
  16. 50
  17. 600
  18. 31
  19. 360
  20. 31
  21. 15
  22. 61
  23. 180
  24. 21
  25. 108
  26. 72
  27. 360
  28. 36
  29. 720
  30. 26
  31. 36
  32. 5
  33. 72
  34. 6
  35. 10
  36. 121
  37. 10
  38. 13
  39. 5
  40. 15

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