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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 978 · 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 12 children or among 14 children, with none left over? (a) 84 (b) 168 (c) 85 (d) 26
  2. 2.Two ribbons are 14 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) 35 cm (c) 7 cm (d) 1 cm
  3. 3.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) 100 (c) 50 (d) 250
  4. 4.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 63 (b) 126 (c) 30 (d) 189
  5. 5.Two ribbons are 18 cm and 48 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) 18 cm (c) 3 cm (d) 30 cm
  6. 6.A teacher has 84 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) 84 (c) 12 (d) 24
  7. 7.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 720 (b) 240 (c) 120 (d) 54
  8. 8.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) 11 cm (b) 1 cm (c) 33 cm (d) 55 cm
  9. 9.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 210 (b) 315 (c) 105 (d) 36
  10. 10.Two ribbons are 20 cm and 32 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) 12 cm (c) 2 cm (d) 4 cm
  11. 11.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) 126 (c) 84 (d) 42
  12. 12.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 36 (b) 216 (c) 72 (d) 30
  13. 13.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 160 (b) 80 (c) 320 (d) 36
  14. 14.Two bells ring every 12 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 216 min (c) 36 min (d) 30 min
  15. 15.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) 20 (b) 10 (c) 5 (d) 30
  16. 16.A teacher has 33 pencils and 44 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 33 (b) 11 (c) 1 (d) 132
  17. 17.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) 60 min (b) 2 min (c) 16 min (d) 30 min
  18. 18.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) 72 min (c) 432 min (d) 42 min
  19. 19.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) 14 min (c) 2 min (d) 40 min
  20. 20.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) 24 min (b) 140 min (c) 70 min (d) 2 min
  21. 21.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) 140 min (d) 4 min
  22. 22.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) 90 min (c) 48 min (d) 6 min
  23. 23.A teacher has 20 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 10 (c) 5 (d) 70
  24. 24.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 500 min (b) 100 min (c) 5 min (d) 45 min
  25. 25.Two ribbons are 22 cm and 55 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 11 cm (b) 33 cm (c) 1 cm (d) 22 cm
  26. 26.Two ribbons are 36 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) 36 cm (b) 180 cm (c) 3 cm (d) 9 cm
  27. 27.A teacher has 40 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 40 (c) 10 (d) 50
  28. 28.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) 50 min (c) 525 min (d) 105 min
  29. 29.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) 1 (b) 22 (c) 55 (d) 11
  30. 30.Two ribbons are 49 cm and 56 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) 392 cm (c) 7 cm (d) 1 cm
  31. 31.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
  32. 32.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) 55 min (c) 140 min (d) 5 min
  33. 33.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) 5 cm (b) 10 cm (c) 30 cm (d) 40 cm
  34. 34.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) 25 min (b) 30 min (c) 150 min (d) 5 min
  35. 35.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) 3 min (b) 33 min (c) 90 min (d) 270 min
  36. 36.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) 140 (c) 71 (d) 24
  37. 37.A teacher has 12 pencils and 27 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) 12
  38. 38.A teacher has 30 pencils and 36 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) 30 (d) 180
  39. 39.Two ribbons are 24 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) 72 cm (b) 12 cm (c) 6 cm (d) 24 cm
  40. 40.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) 4 (b) 16 (c) 12 (d) 2

Answer key

  1. 84
  2. 7 cm
  3. 50
  4. 63
  5. 6 cm
  6. 12
  7. 120
  8. 11 cm
  9. 105
  10. 4 cm
  11. 42
  12. 36
  13. 80
  14. 36 min
  15. 10
  16. 11
  17. 30 min
  18. 72 min
  19. 20 min
  20. 70 min
  21. 140 min
  22. 90 min
  23. 10
  24. 100 min
  25. 11 cm
  26. 9 cm
  27. 10
  28. 105 min
  29. 11
  30. 7 cm
  31. 30
  32. 140 min
  33. 10 cm
  34. 30 min
  35. 90 min
  36. 70
  37. 3
  38. 6
  39. 12 cm
  40. 4

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