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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 727 · 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.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 540 (b) 48 (c) 90 (d) 180
  2. 2.Two ribbons are 12 cm and 27 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) 12 cm (c) 15 cm (d) 1 cm
  3. 3.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) 5 min (b) 50 min (c) 250 min (d) 35 min
  4. 4.A teacher has 27 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 108 (c) 27 (d) 3
  5. 5.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) 220 (b) 11 (c) 1 (d) 44
  6. 6.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 90 (b) 135 (c) 45 (d) 24
  7. 7.A teacher has 30 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 5 (c) 1 (d) 210
  8. 8.A teacher has 18 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 18 (c) 63 (d) 3
  9. 9.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 300 (b) 55 (c) 750 (d) 150
  10. 10.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) 105 (c) 210 (d) 315
  11. 11.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) 11 cm (b) 462 cm (c) 1 cm (d) 66 cm
  12. 12.A teacher has 6 pencils and 27 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) 21 (d) 3
  13. 13.Two ribbons are 40 cm and 45 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 40 cm (b) 5 cm (c) 1 cm (d) 360 cm
  14. 14.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 27 min (c) 180 min (d) 60 min
  15. 15.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) 60 (b) 6 (c) 24 (d) 12
  16. 16.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) 10 (c) 1 (d) 2
  17. 17.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) 112 (c) 44 (d) 224
  18. 18.A teacher has 4 pencils and 18 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) 14 (d) 2
  19. 19.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) 5 cm (b) 15 cm (c) 1 cm (d) 25 cm
  20. 20.Two bells ring every 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 28 min (b) 2 min (c) 18 min (d) 56 min
  21. 21.Two ribbons are 8 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) 4 cm (b) 8 cm (c) 20 cm (d) 2 cm
  22. 22.Two ribbons are 30 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) 30 cm (b) 50 cm (c) 5 cm (d) 10 cm
  23. 23.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 18 (b) 54 (c) 15 (d) 36
  24. 24.Two ribbons are 44 cm and 99 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) 44 cm (c) 11 cm (d) 1 cm
  25. 25.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 20 (b) 43 (c) 84 (d) 42
  26. 26.A teacher has 32 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 32 (b) 8 (c) 24 (d) 4
  27. 27.A teacher has 12 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 12 (c) 18 (d) 3
  28. 28.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) 57 (d) 56
  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) 2 cm (c) 1 cm (d) 4 cm
  30. 30.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) 270 min (c) 90 min (d) 33 min
  31. 31.Two bells ring every 8 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 28 min (c) 4 min (d) 160 min
  32. 32.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 36 (b) 80 (c) 320 (d) 160
  33. 33.Two ribbons are 8 cm and 36 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) 2 cm (c) 8 cm (d) 28 cm
  34. 34.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) 9 (d) 3
  35. 35.A teacher has 14 pencils and 16 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) 112 (d) 2
  36. 36.A teacher has 12 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 30 (c) 3 (d) 6
  37. 37.A teacher has 24 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 24 (c) 216 (d) 1
  38. 38.A teacher has 24 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 24 (c) 6 (d) 12
  39. 39.Two ribbons are 9 cm and 12 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 9 cm (b) 3 cm (c) 1 cm (d) 36 cm
  40. 40.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 63 (b) 30 (c) 126 (d) 189

Answer key

  1. 90
  2. 3 cm
  3. 50 min
  4. 9
  5. 11
  6. 45
  7. 5
  8. 9
  9. 150
  10. 105
  11. 11 cm
  12. 3
  13. 5 cm
  14. 60 min
  15. 12
  16. 2
  17. 112
  18. 2
  19. 5 cm
  20. 28 min
  21. 4 cm
  22. 10 cm
  23. 18
  24. 11 cm
  25. 42
  26. 8
  27. 6
  28. 56
  29. 2 cm
  30. 90 min
  31. 40 min
  32. 80
  33. 4 cm
  34. 9
  35. 2
  36. 6
  37. 3
  38. 12
  39. 3 cm
  40. 63

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