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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 329 · 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 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 10 min (c) 12 min (d) 2 min
  2. 2.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 33 min (c) 252 min (d) 3 min
  3. 3.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) 135 (c) 45 (d) 90
  4. 4.A teacher has 6 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 1 (c) 3 (d) 15
  5. 5.A teacher has 70 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 70 (c) 5 (d) 560
  6. 6.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) 4 min (c) 448 min (d) 112 min
  7. 7.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 140 (b) 71 (c) 24 (d) 70
  8. 8.Two ribbons are 21 cm and 56 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) 35 cm (c) 21 cm (d) 1 cm
  9. 9.A teacher has 33 pencils and 44 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 33 (b) 1 (c) 11 (d) 132
  10. 10.A teacher has 63 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 504 (b) 9 (c) 3 (d) 63
  11. 11.A teacher has 6 pencils and 8 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 6 (c) 24 (d) 1
  12. 12.Two ribbons are 4 cm and 6 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) 4 cm (c) 2 cm (d) 1 cm
  13. 13.A teacher has 30 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 30 (c) 50 (d) 5
  14. 14.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 240 (b) 720 (c) 54 (d) 120
  15. 15.A teacher has 10 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 1 (c) 10 (d) 2
  16. 16.A teacher has 6 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 1 (c) 6 (d) 2
  17. 17.A teacher has 8 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 8 (c) 2 (d) 1
  18. 18.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 57 (b) 22 (c) 112 (d) 56
  19. 19.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 60 (b) 756 (c) 252 (d) 126
  20. 20.A teacher has 30 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 3 (c) 24 (d) 30
  21. 21.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 36 (b) 216 (c) 30 (d) 72
  22. 22.Two ribbons are 21 cm and 28 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 21 cm (b) 7 cm (c) 1 cm (d) 84 cm
  23. 23.Two ribbons are 24 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) 4 cm (b) 8 cm (c) 16 cm (d) 24 cm
  24. 24.A teacher has 24 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 12 (c) 6 (d) 72
  25. 25.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) 61 (c) 120 (d) 60
  26. 26.A teacher has 96 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 96 (c) 12 (d) 864
  27. 27.A teacher has 16 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 56 (b) 8 (c) 4 (d) 16
  28. 28.Two ribbons are 96 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) 864 cm (b) 12 cm (c) 6 cm (d) 96 cm
  29. 29.A teacher has 36 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 48 (c) 6 (d) 36
  30. 30.Two ribbons are 66 cm and 77 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 66 cm (b) 462 cm (c) 11 cm (d) 1 cm
  31. 31.A teacher has 49 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 14 (c) 7 (d) 49
  32. 32.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 45 (b) 500 (c) 200 (d) 100
  33. 33.A teacher has 20 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 10 (c) 60 (d) 20
  34. 34.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 224 min (c) 56 min (d) 4 min
  35. 35.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 30 (b) 25 (c) 60 (d) 150
  36. 36.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 30 (b) 16 (c) 60 (d) 31
  37. 37.A teacher has 9 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 9 (c) 1 (d) 3
  38. 38.A teacher has 36 pencils and 45 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) 180 (d) 9
  39. 39.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 44 min (b) 120 min (c) 4 min (d) 480 min
  40. 40.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 56 (b) 18 (c) 28 (d) 29

Answer key

  1. 12 min
  2. 84 min
  3. 45
  4. 3
  5. 10
  6. 112 min
  7. 70
  8. 7 cm
  9. 11
  10. 9
  11. 2
  12. 2 cm
  13. 10
  14. 120
  15. 2
  16. 2
  17. 2
  18. 56
  19. 126
  20. 6
  21. 36
  22. 7 cm
  23. 8 cm
  24. 12
  25. 60
  26. 12
  27. 8
  28. 12 cm
  29. 12
  30. 11 cm
  31. 7
  32. 100
  33. 10
  34. 56 min
  35. 30
  36. 30
  37. 3
  38. 9
  39. 120 min
  40. 28

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