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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 99 · 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 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) 168 cm (b) 4 cm (c) 2 cm (d) 24 cm
  2. 2.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 48 (b) 96 (c) 24 (d) 20
  3. 3.A teacher has 20 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 60 (c) 20 (d) 5
  4. 4.A teacher has 12 pencils and 54 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) 42 (d) 6
  5. 5.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 42 min (c) 432 min (d) 72 min
  6. 6.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) 30 (c) 126 (d) 63
  7. 7.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 2 min (c) 20 min (d) 42 min
  8. 8.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 48 (b) 180 (c) 540 (d) 90
  9. 9.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 24 min (c) 70 min (d) 140 min
  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) 375 (b) 75 (c) 40 (d) 150
  11. 11.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) 30 (b) 12 (c) 6 (d) 3
  12. 12.A teacher has 35 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 5 (c) 1 (d) 10
  13. 13.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) 1 (b) 9 (c) 3 (d) 36
  14. 14.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) 3 min (d) 135 min
  15. 15.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 30 min (c) 25 min (d) 150 min
  16. 16.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) 42 (c) 43 (d) 84
  17. 17.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) 105 min (b) 525 min (c) 50 min (d) 5 min
  18. 18.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) 56 min (b) 28 min (c) 18 min (d) 2 min
  19. 19.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 85 (c) 84 (d) 168
  20. 20.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 108 (b) 21 (c) 72 (d) 36
  21. 21.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) 25 cm (b) 20 cm (c) 5 cm (d) 1 cm
  22. 22.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) 6 min (d) 360 min
  23. 23.A teacher has 18 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 3 (c) 18 (d) 30
  24. 24.A teacher has 12 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 1 (d) 12
  25. 25.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 14 (b) 24 (c) 48 (d) 25
  26. 26.Two bells ring every 6 minutes and every 9 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 3 min (c) 18 min (d) 15 min
  27. 27.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) 2 (b) 4 (c) 1 (d) 6
  28. 28.A teacher has 16 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 8 (c) 4 (d) 16
  29. 29.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 70 (b) 24 (c) 140 (d) 71
  30. 30.Two ribbons are 12 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) 12 cm (b) 30 cm (c) 6 cm (d) 3 cm
  31. 31.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) 60 (c) 35 (d) 120
  32. 32.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) 9 (b) 3 (c) 6 (d) 1
  33. 33.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 25 (b) 30 (c) 150 (d) 60
  34. 34.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 60 (b) 120 (c) 27 (d) 180
  35. 35.Two ribbons are 25 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) 25 cm (b) 1 cm (c) 5 cm (d) 20 cm
  36. 36.A teacher has 10 pencils and 15 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) 10
  37. 37.A teacher has 30 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 20 (c) 10 (d) 5
  38. 38.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) 16 cm (b) 20 cm (c) 2 cm (d) 4 cm
  39. 39.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 72 (b) 216 (c) 36 (d) 30
  40. 40.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 48 min (b) 560 min (c) 4 min (d) 140 min

Answer key

  1. 4 cm
  2. 24
  3. 10
  4. 6
  5. 72 min
  6. 63
  7. 42 min
  8. 90
  9. 70 min
  10. 75
  11. 6
  12. 5
  13. 3
  14. 45 min
  15. 30 min
  16. 42
  17. 105 min
  18. 28 min
  19. 84
  20. 36
  21. 5 cm
  22. 60 min
  23. 6
  24. 3
  25. 24
  26. 18 min
  27. 2
  28. 8
  29. 70
  30. 6 cm
  31. 60
  32. 3
  33. 30
  34. 60
  35. 5 cm
  36. 5
  37. 10
  38. 4 cm
  39. 36
  40. 140 min

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