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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 51 · 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 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) 1 (b) 3 (c) 6 (d) 9
  2. 2.A teacher has 35 pencils and 49 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) 14
  3. 3.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) 2 cm (c) 4 cm (d) 1 cm
  4. 4.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) 3 min (b) 252 min (c) 33 min (d) 84 min
  5. 5.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) 4 min (b) 160 min (c) 28 min (d) 40 min
  6. 6.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) 6 (c) 1 (d) 2
  7. 7.Two ribbons are 16 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) 16 cm (c) 20 cm (d) 2 cm
  8. 8.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 500 min (b) 5 min (c) 45 min (d) 100 min
  9. 9.A teacher has 9 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
  10. 10.A teacher has 8 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 8 (c) 2 (d) 1
  11. 11.Two ribbons are 44 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) 44 cm (c) 1 cm (d) 33 cm
  12. 12.A teacher has 15 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 25 (b) 1 (c) 15 (d) 5
  13. 13.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 40 (b) 20 (c) 21 (d) 14
  14. 14.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 180 (b) 33 (c) 270 (d) 90
  15. 15.Two bells ring every 6 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 27 min (c) 3 min (d) 126 min
  16. 16.A teacher has 21 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 168 (b) 1 (c) 3 (d) 21
  17. 17.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 168 (b) 84 (c) 336 (d) 40
  18. 18.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) 29 (c) 56 (d) 28
  19. 19.A teacher has 8 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 8 (c) 2 (d) 4
  20. 20.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 200 (b) 45 (c) 100 (d) 500
  21. 21.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) 27 min (b) 180 min (c) 3 min (d) 60 min
  22. 22.Two ribbons are 70 cm and 90 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 70 cm (b) 10 cm (c) 20 cm (d) 5 cm
  23. 23.Two ribbons are 24 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) 2 cm (b) 4 cm (c) 24 cm (d) 168 cm
  24. 24.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 26 min (b) 2 min (c) 84 min (d) 168 min
  25. 25.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 21 (b) 72 (c) 36 (d) 108
  26. 26.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) 12 (b) 3 (c) 36 (d) 6
  27. 27.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) 2 cm (c) 20 cm (d) 8 cm
  28. 28.A teacher has 30 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 10 (c) 40 (d) 5
  29. 29.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) 24 min (b) 45 min (c) 3 min (d) 135 min
  30. 30.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) 224 min (b) 36 min (c) 56 min (d) 4 min
  31. 31.A teacher has 10 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 10 (c) 35 (d) 5
  32. 32.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 3 min (c) 105 min (d) 315 min
  33. 33.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 55 (b) 750 (c) 300 (d) 150
  34. 34.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 168 (b) 85 (c) 84 (d) 26
  35. 35.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 120 (b) 61 (c) 22 (d) 60
  36. 36.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) 6 cm (b) 24 cm (c) 30 cm (d) 3 cm
  37. 37.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) 44 (c) 448 (d) 224
  38. 38.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) 120 (c) 60 (d) 180
  39. 39.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 70 min (b) 45 min (c) 5 min (d) 350 min
  40. 40.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 54 (b) 120 (c) 720 (d) 240

Answer key

  1. 3
  2. 7
  3. 2 cm
  4. 84 min
  5. 40 min
  6. 2
  7. 4 cm
  8. 100 min
  9. 3
  10. 2
  11. 11 cm
  12. 5
  13. 20
  14. 90
  15. 42 min
  16. 3
  17. 84
  18. 28
  19. 4
  20. 100
  21. 60 min
  22. 10 cm
  23. 4 cm
  24. 84 min
  25. 36
  26. 6
  27. 4 cm
  28. 10
  29. 45 min
  30. 56 min
  31. 5
  32. 105 min
  33. 150
  34. 84
  35. 60
  36. 6 cm
  37. 112
  38. 60
  39. 70 min
  40. 120

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