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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 118 · 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 8 children or among 14 children, with none left over? (a) 112 (b) 56 (c) 57 (d) 22
  2. 2.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
  3. 3.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) 15 cm (b) 3 cm (c) 6 cm (d) 1 cm
  4. 4.Two ribbons are 8 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) 24 cm (b) 8 cm (c) 4 cm (d) 2 cm
  5. 5.Two bells ring every 18 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 756 min (b) 126 min (c) 6 min (d) 60 min
  6. 6.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) 10 (b) 6 (c) 1 (d) 2
  7. 7.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) 3 (c) 1 (d) 9
  8. 8.A teacher has 21 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 21 (c) 1 (d) 14
  9. 9.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 54 (b) 168 (c) 504 (d) 84
  10. 10.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 40 (b) 150 (c) 75 (d) 375
  11. 11.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) 20 cm (b) 16 cm (c) 4 cm (d) 2 cm
  12. 12.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
  13. 13.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 28 (b) 160 (c) 80 (d) 40
  14. 14.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) 54 (c) 36 (d) 18
  15. 15.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 16 min (b) 60 min (c) 2 min (d) 30 min
  16. 16.Two bells ring every 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 90 min (c) 540 min (d) 48 min
  17. 17.Two ribbons are 10 cm and 35 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) 5 cm (c) 25 cm (d) 1 cm
  18. 18.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 84 min (c) 336 min (d) 4 min
  19. 19.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) 2 min (d) 12 min
  20. 20.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 48 (b) 280 (c) 140 (d) 560
  21. 21.Two ribbons are 21 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) 1 cm (b) 21 cm (c) 168 cm (d) 3 cm
  22. 22.A teacher has 9 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 1 (c) 36 (d) 3
  23. 23.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) 45 min (b) 350 min (c) 70 min (d) 5 min
  24. 24.Two ribbons are 18 cm and 81 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 18 cm (b) 63 cm (c) 9 cm (d) 3 cm
  25. 25.A teacher has 24 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 24 (c) 3 (d) 6
  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) 120 (b) 60 (c) 32 (d) 240
  27. 27.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) 14 (b) 4 (c) 1 (d) 2
  28. 28.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) 160 min (b) 28 min (c) 4 min (d) 40 min
  29. 29.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 60 min (c) 360 min (d) 6 min
  30. 30.A teacher has 21 pencils and 56 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) 21 (d) 7
  31. 31.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) 180 (c) 90 (d) 48
  32. 32.Two ribbons are 28 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) 28 cm (b) 1 cm (c) 21 cm (d) 7 cm
  33. 33.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 189 (b) 63 (c) 126 (d) 30
  34. 34.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
  35. 35.A teacher has 60 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 12 (c) 60 (d) 6
  36. 36.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 61 (b) 22 (c) 60 (d) 120
  37. 37.Two ribbons are 16 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) 144 cm (c) 2 cm (d) 16 cm
  38. 38.Two bells ring every 8 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 18 min (b) 40 min (c) 2 min (d) 80 min
  39. 39.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) 29 (c) 28 (d) 18
  40. 40.A teacher has 28 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) 4 (c) 8 (d) 28

Answer key

  1. 56
  2. 10
  3. 3 cm
  4. 4 cm
  5. 126 min
  6. 2
  7. 3
  8. 7
  9. 84
  10. 75
  11. 4 cm
  12. 5 cm
  13. 40
  14. 18
  15. 30 min
  16. 90 min
  17. 5 cm
  18. 84 min
  19. 12 min
  20. 140
  21. 3 cm
  22. 3
  23. 70 min
  24. 9 cm
  25. 6
  26. 60
  27. 2
  28. 40 min
  29. 60 min
  30. 7
  31. 90
  32. 7 cm
  33. 63
  34. 72
  35. 12
  36. 60
  37. 2 cm
  38. 40 min
  39. 28
  40. 4

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