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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 916 · 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 ribbons are 35 cm and 49 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) 7 cm (c) 1 cm (d) 35 cm
  2. 2.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 144 (b) 72 (c) 432 (d) 42
  3. 3.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) 216 (c) 24 (d) 1
  4. 4.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) 16 (b) 48 (c) 4 (d) 8
  5. 5.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) 90 (c) 180 (d) 48
  6. 6.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) 35 min (c) 50 min (d) 250 min
  7. 7.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 192 (b) 28 (c) 48 (d) 96
  8. 8.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 168 (b) 504 (c) 84 (d) 54
  9. 9.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 36 (b) 72 (c) 21 (d) 108
  10. 10.Two bells ring every 9 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 21 min (b) 3 min (c) 36 min (d) 108 min
  11. 11.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) 192 min (b) 4 min (c) 28 min (d) 48 min
  12. 12.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) 168 (c) 26 (d) 85
  13. 13.A teacher has 12 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 12 (c) 48 (d) 4
  14. 14.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 320 (b) 36 (c) 160 (d) 80
  15. 15.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 60 (b) 150 (c) 25 (d) 30
  16. 16.A teacher has 12 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) 2 (c) 16 (d) 12
  17. 17.Two ribbons are 20 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) 1 cm (b) 25 cm (c) 5 cm (d) 20 cm
  18. 18.Two ribbons are 32 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) 288 cm (b) 4 cm (c) 32 cm (d) 2 cm
  19. 19.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) 33 min (b) 270 min (c) 90 min (d) 3 min
  20. 20.Two ribbons are 36 cm and 42 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 36 cm (b) 3 cm (c) 252 cm (d) 6 cm
  21. 21.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 300 (b) 35 (c) 120 (d) 60
  22. 22.Two ribbons are 10 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) 10 cm (b) 2 cm (c) 60 cm (d) 1 cm
  23. 23.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) 3 min (c) 45 min (d) 135 min
  24. 24.A teacher has 16 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) 20 (c) 2 (d) 16
  25. 25.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) 33 (b) 1 (c) 22 (d) 11
  26. 26.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 126 (b) 42 (c) 84 (d) 27
  27. 27.A teacher has 25 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 1 (c) 10 (d) 25
  28. 28.A teacher has 30 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) 3 (c) 6 (d) 30
  29. 29.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) 90 (c) 33 (d) 270
  30. 30.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) 1 cm (b) 4 cm (c) 14 cm (d) 2 cm
  31. 31.A teacher has 55 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 22 (b) 11 (c) 1 (d) 55
  32. 32.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 24 (b) 12 (c) 13 (d) 10
  33. 33.Two ribbons are 15 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) 15 cm (c) 1 cm (d) 12 cm
  34. 34.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 70 (c) 45 (d) 350
  35. 35.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 30 (b) 60 (c) 21 (d) 90
  36. 36.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) 2 (b) 16 (c) 20 (d) 4
  37. 37.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) 56 min (c) 2 min (d) 18 min
  38. 38.Two ribbons are 16 cm and 24 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 16 cm (b) 8 cm (c) 4 cm (d) 48 cm
  39. 39.Two bells ring every 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 22 min (b) 56 min (c) 2 min (d) 112 min
  40. 40.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

Answer key

  1. 7 cm
  2. 72
  3. 3
  4. 8
  5. 90
  6. 50 min
  7. 48
  8. 84
  9. 36
  10. 36 min
  11. 48 min
  12. 84
  13. 4
  14. 80
  15. 30
  16. 4
  17. 5 cm
  18. 4 cm
  19. 90 min
  20. 6 cm
  21. 60
  22. 2 cm
  23. 45 min
  24. 4
  25. 11
  26. 42
  27. 5
  28. 6
  29. 90
  30. 2 cm
  31. 11
  32. 12
  33. 3 cm
  34. 70
  35. 30
  36. 4
  37. 28 min
  38. 8 cm
  39. 56 min
  40. 20 min

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