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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 204 · 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 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 45 min (c) 70 min (d) 350 min
  2. 2.A teacher has 25 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 25 (b) 150 (c) 1 (d) 5
  3. 3.A teacher has 40 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 24 (c) 40 (d) 4
  4. 4.Two ribbons are 45 cm and 63 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) 3 cm (c) 9 cm (d) 45 cm
  5. 5.A teacher has 48 pencils and 60 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) 6 (d) 240
  6. 6.A teacher has 24 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 8 (c) 40 (d) 24
  7. 7.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) 540 min (b) 48 min (c) 6 min (d) 90 min
  8. 8.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) 33 min (b) 252 min (c) 84 min (d) 3 min
  9. 9.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) 60 min (b) 27 min (c) 3 min (d) 180 min
  10. 10.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 27 (b) 42 (c) 126 (d) 84
  11. 11.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 700 min (b) 5 min (c) 55 min (d) 140 min
  12. 12.Two ribbons are 33 cm and 88 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 33 cm (b) 55 cm (c) 1 cm (d) 11 cm
  13. 13.A teacher has 8 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 1 (c) 2 (d) 40
  14. 14.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 24 (b) 71 (c) 70 (d) 140
  15. 15.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) 4 cm (b) 48 cm (c) 8 cm (d) 16 cm
  16. 16.A teacher has 18 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 45 (b) 9 (c) 3 (d) 18
  17. 17.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) 28 min (c) 48 min (d) 4 min
  18. 18.A teacher has 44 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 1 (c) 33 (d) 44
  19. 19.Two ribbons are 60 cm and 96 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) 36 cm (c) 60 cm (d) 12 cm
  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) 72 (b) 36 (c) 21 (d) 108
  21. 21.A teacher has 14 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) 14 (c) 1 (d) 112
  22. 22.A teacher has 20 pencils and 25 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) 20 (d) 100
  23. 23.A teacher has 24 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 32 (c) 4 (d) 24
  24. 24.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 126 (b) 252 (c) 756 (d) 60
  25. 25.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 120 min (b) 22 min (c) 60 min (d) 2 min
  26. 26.A teacher has 32 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 32 (b) 8 (c) 4 (d) 24
  27. 27.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 41 (b) 80 (c) 18 (d) 40
  28. 28.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) 30 min (d) 2 min
  29. 29.Two ribbons are 30 cm and 50 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 5 cm (b) 30 cm (c) 20 cm (d) 10 cm
  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) 4 min (b) 224 min (c) 36 min (d) 56 min
  31. 31.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) 30 (d) 36
  32. 32.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 54 (b) 36 (c) 18 (d) 15
  33. 33.A teacher has 22 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
  34. 34.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 60 (b) 300 (c) 35 (d) 120
  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) 21 (b) 90 (c) 30 (d) 60
  36. 36.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 480 (b) 44 (c) 240 (d) 120
  37. 37.Two ribbons are 14 cm and 63 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 49 cm (b) 7 cm (c) 1 cm (d) 14 cm
  38. 38.A teacher has 15 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 1 (c) 3 (d) 9
  39. 39.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) 42 min (b) 6 min (c) 72 min (d) 432 min
  40. 40.A teacher has 6 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 15 (c) 3 (d) 6

Answer key

  1. 70 min
  2. 5
  3. 8
  4. 9 cm
  5. 12
  6. 8
  7. 90 min
  8. 84 min
  9. 60 min
  10. 42
  11. 140 min
  12. 11 cm
  13. 2
  14. 70
  15. 8 cm
  16. 9
  17. 48 min
  18. 11
  19. 12 cm
  20. 36
  21. 2
  22. 5
  23. 8
  24. 126
  25. 60 min
  26. 8
  27. 40
  28. 30 min
  29. 10 cm
  30. 56 min
  31. 36
  32. 18
  33. 11
  34. 60
  35. 30
  36. 120
  37. 7 cm
  38. 3
  39. 72 min
  40. 3

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