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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 529 · 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 1 when divided by 8, 3 or 10.
  2. 2.Vivaan takes 48 seconds and Kavya 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 15 that leaves a remainder of 1 when divided by 4, 15 or 12.
  4. 4.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 4.
  5. 5.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Two tanks hold 70 litres and 40 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 12 that leaves a remainder of 1 when divided by 12, 3 or 4.
  8. 8.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 10 or 9.
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 3 or 15.
  10. 10.Diya takes 80 seconds and Karan 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?
  11. 11.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?
  12. 12.Two tanks hold 120 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Two tanks hold 225 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Two tanks hold 225 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 8, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Kavya takes 36 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?
  17. 17.Three temple bells ring every 6, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 20, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Kabir takes 50 seconds and Karan 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?
  20. 20.Two tanks hold 50 litres and 175 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 45 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?
  22. 22.Vivaan takes 36 seconds and Meera 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?
  23. 23.Three temple bells ring every 10, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 125 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Two tanks hold 60 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Karan takes 30 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?
  27. 27.A hall floor is 200 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Two tanks hold 20 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.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?
  30. 30.Three temple bells ring every 8, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 3 or 15.
  34. 34.Vivaan takes 48 seconds and Kavya 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?
  35. 35.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 10 or 9.
  36. 36.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 5 or 6.
  37. 37.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?
  38. 38.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 9 or 10.
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 8.
  40. 40.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 8 or 5.

Answer key

  1. 121
  2. 240
  3. 61
  4. 62
  5. 56
  6. 10
  7. 13
  8. 182
  9. 47
  10. 720
  11. 30
  12. 30
  13. 45
  14. 25
  15. 120
  16. 144
  17. 90
  18. 60
  19. 150
  20. 25
  21. 180
  22. 720
  23. 20
  24. 25
  25. 20
  26. 180
  27. 10
  28. 10
  29. 15
  30. 120
  31. 24
  32. 12
  33. 46
  34. 240
  35. 181
  36. 32
  37. 40
  38. 92
  39. 121
  40. 43

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