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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 59 · 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 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) 2 min (b) 16 min (c) 30 min (d) 60 min
  2. 2.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 84 (b) 504 (c) 168 (d) 54
  3. 3.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 48 (b) 96 (c) 192 (d) 28
  4. 4.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) 6 (b) 48 (c) 60 (d) 12
  5. 5.Two ribbons are 24 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) 8 cm (b) 24 cm (c) 4 cm (d) 16 cm
  6. 6.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) 60 min (c) 6 min (d) 126 min
  7. 7.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) 126 (c) 30 (d) 63
  8. 8.A teacher has 18 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 27 (c) 18 (d) 9
  9. 9.Two ribbons are 25 cm and 30 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) 5 cm (c) 25 cm (d) 150 cm
  10. 10.A teacher has 50 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 30 (c) 5 (d) 10
  11. 11.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 35 (b) 250 (c) 50 (d) 100
  12. 12.Two ribbons are 12 cm and 20 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) 12 cm (c) 2 cm (d) 8 cm
  13. 13.Two ribbons are 6 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) 1 cm (b) 21 cm (c) 3 cm (d) 6 cm
  14. 14.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 42 (b) 20 (c) 43 (d) 84
  15. 15.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) 336 min (b) 84 min (c) 40 min (d) 4 min
  16. 16.Two ribbons are 88 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) 88 cm (b) 1 cm (c) 11 cm (d) 792 cm
  17. 17.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 105 (b) 210 (c) 525 (d) 50
  18. 18.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 240 (b) 44 (c) 480 (d) 120
  19. 19.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 375 (b) 40 (c) 75 (d) 150
  20. 20.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 55 (b) 140 (c) 280 (d) 700
  21. 21.A teacher has 16 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 16 (c) 144 (d) 2
  22. 22.Two ribbons are 33 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) 44 cm (b) 33 cm (c) 11 cm (d) 1 cm
  23. 23.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) 12 (b) 2 (c) 16 (d) 4
  24. 24.A teacher has 50 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 50 (c) 10 (d) 20
  25. 25.A teacher has 40 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 8 (c) 40 (d) 4
  26. 26.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) 20 min (b) 2 min (c) 14 min (d) 40 min
  27. 27.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) 10 (c) 12 (d) 13
  28. 28.Two ribbons are 15 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) 6 cm (b) 3 cm (c) 1 cm (d) 15 cm
  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) 45 min (b) 24 min (c) 135 min (d) 3 min
  30. 30.Two ribbons are 30 cm and 70 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) 30 cm (d) 10 cm
  31. 31.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 80 (b) 40 (c) 41 (d) 18
  32. 32.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 24 (b) 20 (c) 96 (d) 48
  33. 33.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 105 min (c) 50 min (d) 525 min
  34. 34.A teacher has 18 pencils and 24 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) 72
  35. 35.A teacher has 66 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 66 (b) 462 (c) 1 (d) 11
  36. 36.A teacher has 56 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 56 (b) 8 (c) 16 (d) 4
  37. 37.Two bells ring every 12 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 32 min (c) 4 min (d) 240 min
  38. 38.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) 12 (b) 18 (c) 3 (d) 6
  39. 39.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) 180 min (b) 27 min (c) 60 min (d) 3 min
  40. 40.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) 4 cm (b) 1 cm (c) 2 cm (d) 14 cm

Answer key

  1. 30 min
  2. 84
  3. 48
  4. 12
  5. 8 cm
  6. 126 min
  7. 63
  8. 9
  9. 5 cm
  10. 10
  11. 50
  12. 4 cm
  13. 3 cm
  14. 42
  15. 84 min
  16. 11 cm
  17. 105
  18. 120
  19. 75
  20. 140
  21. 2
  22. 11 cm
  23. 4
  24. 10
  25. 8
  26. 20 min
  27. 12
  28. 3 cm
  29. 45 min
  30. 10 cm
  31. 40
  32. 24
  33. 105 min
  34. 6
  35. 11
  36. 8
  37. 60 min
  38. 6
  39. 60 min
  40. 2 cm

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