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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 878 · 40 questions
TalentJR

How to solve it (Together again or cut equally?): “Ring together again”, “smallest number both divide” → LCM: count in the bigger number until the smaller one divides it. “Longest equal pieces”, “greatest number of identical packs” → HCF: list the factors and pick the greatest common one. Check: the LCM is divisible by both numbers; the HCF divides both numbers.

NameDateTime takenScore ___ / 40
  1. 1.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 96 min (b) 20 min (c) 24 min (d) 4 min
  2. 2.A teacher has 8 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 2 (c) 24 (d) 4
  3. 3.A teacher has 63 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 9 (c) 63 (d) 18
  4. 4.A teacher has 24 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 6 (c) 12 (d) 60
  5. 5.A teacher has 30 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 18 (c) 6 (d) 3
  6. 6.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 55 (b) 280 (c) 140 (d) 700
  7. 7.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 61 (b) 120 (c) 60 (d) 22
  8. 8.A teacher has 44 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 44 (b) 1 (c) 220 (d) 11
  9. 9.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 50 min (c) 105 min (d) 525 min
  10. 10.Two bells ring every 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 135 min (b) 24 min (c) 3 min (d) 45 min
  11. 11.A teacher has 20 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 20 (c) 70 (d) 5
  12. 12.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 6 min (c) 120 min (d) 720 min
  13. 13.Two ribbons are 4 cm and 14 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 10 cm (b) 4 cm (c) 2 cm (d) 1 cm
  14. 14.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 85 (b) 168 (c) 84 (d) 26
  15. 15.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 40 (b) 150 (c) 375 (d) 75
  16. 16.Two ribbons are 12 cm and 42 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 12 cm (b) 3 cm (c) 6 cm (d) 30 cm
  17. 17.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 27 (b) 180 (c) 120 (d) 60
  18. 18.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 100 (b) 50 (c) 35 (d) 250
  19. 19.A teacher has 22 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 22 (c) 77 (d) 11
  20. 20.Two bells ring every 12 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 504 min (b) 54 min (c) 84 min (d) 6 min
  21. 21.Two ribbons are 15 cm and 18 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 90 cm (b) 3 cm (c) 15 cm (d) 1 cm
  22. 22.A teacher has 80 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 720 (b) 10 (c) 80 (d) 5
  23. 23.Two ribbons are 21 cm and 24 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 3 cm (b) 168 cm (c) 21 cm (d) 1 cm
  24. 24.Two ribbons are 12 cm and 30 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 6 cm (b) 18 cm (c) 12 cm (d) 3 cm
  25. 25.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 70 (b) 350 (c) 140 (d) 45
  26. 26.A teacher has 40 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 24 (c) 8 (d) 40
  27. 27.Two ribbons are 25 cm and 40 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 25 cm (b) 5 cm (c) 15 cm (d) 1 cm
  28. 28.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 21 min (c) 30 min (d) 90 min
  29. 29.Two ribbons are 4 cm and 18 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 14 cm (b) 4 cm (c) 2 cm (d) 1 cm
  30. 30.Two ribbons are 14 cm and 35 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 7 cm (b) 1 cm (c) 14 cm (d) 21 cm
  31. 31.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 56 (b) 112 (c) 22 (d) 57
  32. 32.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 50 min (b) 35 min (c) 250 min (d) 5 min
  33. 33.Two ribbons are 48 cm and 108 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 60 cm (b) 6 cm (c) 12 cm (d) 48 cm
  34. 34.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 30 (b) 216 (c) 36 (d) 72
  35. 35.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 50 (b) 525 (c) 105 (d) 210
  36. 36.A teacher has 48 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 36 (c) 6 (d) 12
  37. 37.A teacher has 15 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 3 (c) 15 (d) 6
  38. 38.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 112 (b) 224 (c) 448 (d) 44
  39. 39.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 10 (c) 24 (d) 13
  40. 40.Two bells ring every 15 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 270 min (b) 90 min (c) 3 min (d) 33 min

Answer key

  1. 24 min
  2. 4
  3. 9
  4. 12
  5. 6
  6. 140
  7. 60
  8. 11
  9. 105 min
  10. 45 min
  11. 10
  12. 120 min
  13. 2 cm
  14. 84
  15. 75
  16. 6 cm
  17. 60
  18. 50
  19. 11
  20. 84 min
  21. 3 cm
  22. 10
  23. 3 cm
  24. 6 cm
  25. 70
  26. 8
  27. 5 cm
  28. 30 min
  29. 2 cm
  30. 7 cm
  31. 56
  32. 50 min
  33. 12 cm
  34. 36
  35. 105
  36. 12
  37. 3
  38. 112
  39. 12
  40. 90 min

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