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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 506 · 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 12 that leaves a remainder of 2 when divided by 8, 12 or 6.
  2. 2.Three temple bells ring every 4, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Rohan takes 90 seconds and Arjun 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?
  4. 4.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?
  5. 5.Two tanks hold 280 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Two tanks hold 100 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 4 or 15.
  8. 8.Two tanks hold 105 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Kavya takes 40 seconds and Rohan 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?
  10. 10.Dev takes 50 seconds and Manav 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?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 9, 10 or 15.
  12. 12.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 4 or 6.
  13. 13.Aditya takes 45 seconds and Rahul 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?
  14. 14.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?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 9 when divided by 15, 10 or 12.
  16. 16.Arjun takes 72 seconds and Kavya 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?
  17. 17.Karan takes 80 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?
  18. 18.Diya takes 72 seconds and Kabir 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?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 3.
  20. 20.Three temple bells ring every 15, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 4.
  23. 23.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 12 or 15.
  25. 25.Sneha takes 36 seconds and Tara 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?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 10, 6 or 12.
  27. 27.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Three temple bells ring every 10, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Kabir takes 40 seconds and Rahul 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?
  30. 30.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 8 or 15.
  32. 32.Two tanks hold 60 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Two tanks hold 30 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Two tanks hold 350 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Tara takes 60 seconds and Aarav 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?
  36. 36.Two tanks hold 35 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.A hall floor is 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Two tanks hold 50 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Priya takes 40 seconds and Aarav 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?
  40. 40.Three temple bells ring every 9, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 26
  2. 60
  3. 450
  4. 40
  5. 40
  6. 20
  7. 61
  8. 15
  9. 120
  10. 450
  11. 95
  12. 13
  13. 720
  14. 21
  15. 69
  16. 360
  17. 240
  18. 360
  19. 31
  20. 90
  21. 42
  22. 26
  23. 14
  24. 63
  25. 180
  26. 62
  27. 28
  28. 120
  29. 200
  30. 20
  31. 121
  32. 10
  33. 15
  34. 50
  35. 300
  36. 5
  37. 40
  38. 25
  39. 360
  40. 72

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