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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 419 · 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.A teacher has 22 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 55 (c) 22 (d) 11
  2. 2.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) 54 min (b) 504 min (c) 6 min (d) 84 min
  3. 3.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) 77 (b) 11 (c) 22 (d) 1
  4. 4.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) 3 min (b) 33 min (c) 90 min (d) 270 min
  5. 5.Two ribbons are 6 cm and 9 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) 3 cm (c) 18 cm (d) 1 cm
  6. 6.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 432 (b) 42 (c) 144 (d) 72
  7. 7.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 60 (b) 21 (c) 30 (d) 90
  8. 8.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 33 (b) 252 (c) 168 (d) 84
  9. 9.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 18 (b) 56 (c) 28 (d) 29
  10. 10.A teacher has 8 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 2 (c) 8 (d) 28
  11. 11.A teacher has 12 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 3 (c) 12 (d) 6
  12. 12.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 210 (b) 105 (c) 50 (d) 525
  13. 13.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 44 min (b) 112 min (c) 448 min (d) 4 min
  14. 14.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 10 min (c) 12 min (d) 24 min
  15. 15.A teacher has 10 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 5 (c) 1 (d) 30
  16. 16.Two ribbons are 6 cm and 8 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 1 cm (b) 24 cm (c) 6 cm (d) 2 cm
  17. 17.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 15 (b) 18 (c) 36 (d) 54
  18. 18.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 448 (b) 224 (c) 44 (d) 112
  19. 19.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 90 (c) 45 (d) 135
  20. 20.Two bells ring every 12 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 30 min (c) 6 min (d) 216 min
  21. 21.Two bells ring every 4 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 14 min (c) 20 min (d) 2 min
  22. 22.A teacher has 35 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 1 (c) 7 (d) 28
  23. 23.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) 3 cm (b) 6 cm (c) 12 cm (d) 18 cm
  24. 24.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 756 (b) 60 (c) 252 (d) 126
  25. 25.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 36 (b) 315 (c) 105 (d) 210
  26. 26.Two ribbons are 48 cm and 54 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) 48 cm (c) 432 cm (d) 6 cm
  27. 27.A teacher has 16 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 40 (c) 8 (d) 4
  28. 28.Two bells ring every 6 minutes and every 9 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 15 min (c) 18 min (d) 54 min
  29. 29.A teacher has 4 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 2 (c) 1 (d) 4
  30. 30.Two ribbons are 6 cm and 10 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) 1 cm (c) 4 cm (d) 2 cm
  31. 31.Two ribbons are 24 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) 24 cm (b) 6 cm (c) 120 cm (d) 3 cm
  32. 32.Two ribbons are 24 cm and 54 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) 24 cm (c) 30 cm (d) 6 cm
  33. 33.A teacher has 25 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 150 (c) 25 (d) 5
  34. 34.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 22 (b) 120 (c) 61 (d) 60
  35. 35.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 71 (b) 70 (c) 24 (d) 140
  36. 36.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 42 (b) 20 (c) 43 (d) 84
  37. 37.A teacher has 6 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 6 (d) 1
  38. 38.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 120 (b) 480 (c) 44 (d) 240
  39. 39.A teacher has 15 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 5 (c) 15 (d) 10
  40. 40.Two bells ring every 8 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 18 min (c) 80 min (d) 2 min

Answer key

  1. 11
  2. 84 min
  3. 11
  4. 90 min
  5. 3 cm
  6. 72
  7. 30
  8. 84
  9. 28
  10. 4
  11. 6
  12. 105
  13. 112 min
  14. 12 min
  15. 5
  16. 2 cm
  17. 18
  18. 112
  19. 45
  20. 36 min
  21. 20 min
  22. 7
  23. 6 cm
  24. 126
  25. 105
  26. 6 cm
  27. 8
  28. 18 min
  29. 2
  30. 2 cm
  31. 6 cm
  32. 6 cm
  33. 5
  34. 60
  35. 70
  36. 42
  37. 3
  38. 120
  39. 5
  40. 40 min

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