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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 135 · 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 9 children or among 15 children, with none left over? (a) 135 (b) 45 (c) 24 (d) 90
  2. 2.A teacher has 21 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 21 (c) 1 (d) 7
  3. 3.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 48 (b) 25 (c) 14 (d) 24
  4. 4.Two ribbons are 18 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) 3 cm (b) 54 cm (c) 9 cm (d) 18 cm
  5. 5.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 57 (b) 112 (c) 22 (d) 56
  6. 6.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) 14 min (b) 2 min (c) 20 min (d) 40 min
  7. 7.Two ribbons are 9 cm and 15 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 3 cm (b) 6 cm (c) 1 cm (d) 9 cm
  8. 8.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) 6 (b) 3 (c) 18 (d) 72
  9. 9.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 21 (b) 72 (c) 36 (d) 108
  10. 10.A teacher has 30 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 30 (c) 3 (d) 6
  11. 11.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) 80 min (b) 40 min (c) 18 min (d) 2 min
  12. 12.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 180 (b) 33 (c) 270 (d) 90
  13. 13.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) 4 (b) 40 (c) 8 (d) 24
  14. 14.Two ribbons are 77 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) 1 cm (b) 77 cm (c) 11 cm (d) 616 cm
  15. 15.A teacher has 14 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) 14 (c) 21 (d) 1
  16. 16.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) 60 (d) 30
  17. 17.A teacher has 36 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 3 (c) 9 (d) 27
  18. 18.A teacher has 42 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 336 (c) 6 (d) 42
  19. 19.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) 11 (b) 1 (c) 22 (d) 55
  20. 20.A teacher has 14 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) 1 (c) 2 (d) 4
  21. 21.A teacher has 33 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 33 (b) 22 (c) 11 (d) 1
  22. 22.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) 135 min (b) 45 min (c) 3 min (d) 24 min
  23. 23.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
  24. 24.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) 120 (c) 35 (d) 60
  25. 25.A teacher has 55 pencils and 88 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 55 (c) 33 (d) 11
  26. 26.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) 3 cm (b) 1 cm (c) 21 cm (d) 168 cm
  27. 27.Two bells ring every 18 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 126 min (b) 3 min (c) 378 min (d) 39 min
  28. 28.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 120 (b) 22 (c) 61 (d) 60
  29. 29.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 3 min (c) 105 min (d) 315 min
  30. 30.A teacher has 10 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) 8 (c) 2 (d) 10
  31. 31.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) 50 min (b) 5 min (c) 105 min (d) 525 min
  32. 32.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) 6 (b) 3 (c) 30 (d) 180
  33. 33.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) 240 min (b) 4 min (c) 32 min (d) 60 min
  34. 34.A teacher has 15 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 25 (c) 15 (d) 5
  35. 35.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 120 (b) 60 (c) 42 (d) 360
  36. 36.Two ribbons are 6 cm and 15 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) 9 cm (c) 1 cm (d) 3 cm
  37. 37.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 150 min (b) 750 min (c) 55 min (d) 5 min
  38. 38.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) 45 min (d) 5 min
  39. 39.Two ribbons are 27 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) 108 cm (b) 27 cm (c) 9 cm (d) 3 cm
  40. 40.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 72 (b) 432 (c) 144 (d) 42

Answer key

  1. 45
  2. 7
  3. 24
  4. 9 cm
  5. 56
  6. 20 min
  7. 3 cm
  8. 6
  9. 36
  10. 6
  11. 40 min
  12. 90
  13. 8
  14. 11 cm
  15. 7
  16. 30
  17. 9
  18. 6
  19. 11
  20. 2
  21. 11
  22. 45 min
  23. 60 min
  24. 60
  25. 11
  26. 3 cm
  27. 126 min
  28. 60
  29. 105 min
  30. 2
  31. 105 min
  32. 6
  33. 60 min
  34. 5
  35. 60
  36. 3 cm
  37. 150 min
  38. 100 min
  39. 9 cm
  40. 72

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