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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 970 · 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 55 pencils and 66 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 1 (c) 330 (d) 55
  2. 2.Two ribbons are 10 cm and 15 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 5 cm (b) 30 cm (c) 1 cm (d) 10 cm
  3. 3.A teacher has 6 pencils and 9 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 6 (c) 18 (d) 1
  4. 4.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 13 (b) 24 (c) 10 (d) 12
  5. 5.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) 36 (c) 72 (d) 216
  6. 6.A teacher has 16 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 48 (c) 16 (d) 8
  7. 7.Two ribbons are 10 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
  8. 8.Two ribbons are 50 cm and 80 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) 30 cm (c) 5 cm (d) 50 cm
  9. 9.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 2 min (c) 42 min (d) 20 min
  10. 10.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 84 (b) 85 (c) 168 (d) 26
  11. 11.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) 2 (d) 6
  12. 12.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) 6 min (b) 36 min (c) 216 min (d) 30 min
  13. 13.Two ribbons are 14 cm and 16 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) 14 cm (c) 112 cm (d) 2 cm
  14. 14.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 22 (b) 112 (c) 56 (d) 57
  15. 15.Two ribbons are 6 cm and 21 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) 15 cm (c) 3 cm (d) 6 cm
  16. 16.A teacher has 60 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 12 (c) 6 (d) 36
  17. 17.Two ribbons are 10 cm and 25 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) 10 cm (c) 15 cm (d) 5 cm
  18. 18.A teacher has 70 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) 70 (c) 20 (d) 5
  19. 19.Two ribbons are 8 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) 10 cm (b) 2 cm (c) 1 cm (d) 8 cm
  20. 20.Two ribbons are 33 cm and 88 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 55 cm (b) 33 cm (c) 11 cm (d) 1 cm
  21. 21.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 40 (b) 18 (c) 41 (d) 80
  22. 22.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 28 min (b) 48 min (c) 192 min (d) 4 min
  23. 23.A teacher has 33 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 33 (c) 1 (d) 22
  24. 24.A teacher has 45 pencils and 63 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) 18 (d) 45
  25. 25.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 30 min (b) 63 min (c) 3 min (d) 189 min
  26. 26.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 60 (b) 240 (c) 32 (d) 120
  27. 27.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 48 (b) 14 (c) 25 (d) 24
  28. 28.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 180 (b) 48 (c) 540 (d) 90
  29. 29.A teacher has 20 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 4 (c) 2 (d) 20
  30. 30.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 70 min (b) 2 min (c) 140 min (d) 24 min
  31. 31.A teacher has 49 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 392 (c) 1 (d) 49
  32. 32.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) 6 (b) 9 (c) 1 (d) 3
  33. 33.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 120 (b) 240 (c) 54 (d) 720
  34. 34.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 60 (b) 30 (c) 16 (d) 31
  35. 35.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) 54 (d) 36
  36. 36.A teacher has 14 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 1 (c) 4 (d) 14
  37. 37.Two ribbons are 8 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) 8 cm (b) 2 cm (c) 1 cm (d) 6 cm
  38. 38.A teacher has 16 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 16 (c) 12 (d) 2
  39. 39.A teacher has 72 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 648 (b) 72 (c) 3 (d) 9
  40. 40.A teacher has 30 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 20 (c) 10 (d) 5

Answer key

  1. 11
  2. 5 cm
  3. 3
  4. 12
  5. 36
  6. 8
  7. 2 cm
  8. 10 cm
  9. 42 min
  10. 84
  11. 2
  12. 36 min
  13. 2 cm
  14. 56
  15. 3 cm
  16. 12
  17. 5 cm
  18. 10
  19. 2 cm
  20. 11 cm
  21. 40
  22. 48 min
  23. 11
  24. 9
  25. 63 min
  26. 60
  27. 24
  28. 90
  29. 4
  30. 70 min
  31. 7
  32. 3
  33. 120
  34. 30
  35. 18
  36. 2
  37. 2 cm
  38. 4
  39. 9
  40. 10

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