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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 915 · 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 16 children or among 20 children, with none left over? (a) 160 (b) 320 (c) 80 (d) 36
  2. 2.Two ribbons are 10 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) 5 cm (b) 30 cm (c) 10 cm (d) 1 cm
  3. 3.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) 3 min (b) 18 min (c) 15 min (d) 54 min
  4. 4.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 24 min (c) 10 min (d) 12 min
  5. 5.Two ribbons are 28 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) 21 cm (b) 28 cm (c) 7 cm (d) 1 cm
  6. 6.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) 10 cm (b) 5 cm (c) 20 cm (d) 30 cm
  7. 7.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) 60 min (b) 22 min (c) 120 min (d) 2 min
  8. 8.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
  9. 9.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) 24 cm (d) 6 cm
  10. 10.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) 150 cm (c) 5 cm (d) 25 cm
  11. 11.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 29 (b) 56 (c) 18 (d) 28
  12. 12.Two ribbons are 18 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) 18 cm (b) 126 cm (c) 1 cm (d) 3 cm
  13. 13.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
  14. 14.A teacher has 18 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 18 (c) 3 (d) 63
  15. 15.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) 21 (b) 1 (c) 7 (d) 28
  16. 16.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) 42 min (b) 20 min (c) 84 min (d) 2 min
  17. 17.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 150 (b) 375 (c) 75 (d) 40
  18. 18.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) 24 (c) 90 (d) 45
  19. 19.Two ribbons are 32 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) 160 cm (c) 4 cm (d) 32 cm
  20. 20.A teacher has 21 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 7 (c) 14 (d) 21
  21. 21.A teacher has 16 pencils and 56 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) 8 (d) 40
  22. 22.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) 10 (b) 30 (c) 5 (d) 20
  23. 23.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 375 min (b) 40 min (c) 5 min (d) 75 min
  24. 24.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) 11 (b) 66 (c) 1 (d) 462
  25. 25.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) 40 (b) 8 (c) 1 (d) 2
  26. 26.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 55 (b) 750 (c) 150 (d) 300
  27. 27.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 60 (b) 25 (c) 150 (d) 30
  28. 28.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) 90 min (d) 6 min
  29. 29.A teacher has 10 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 25 (b) 10 (c) 1 (d) 5
  30. 30.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 112 min (b) 44 min (c) 448 min (d) 4 min
  31. 31.Two ribbons are 35 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) 35 cm (b) 21 cm (c) 1 cm (d) 7 cm
  32. 32.A teacher has 36 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 12 (c) 6 (d) 144
  33. 33.A teacher has 30 pencils and 80 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) 30 (d) 10
  34. 34.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 40 (b) 28 (c) 160 (d) 80
  35. 35.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) 15 (c) 36 (d) 18
  36. 36.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) 27 min (b) 180 min (c) 3 min (d) 60 min
  37. 37.A teacher has 20 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 16 (c) 2 (d) 4
  38. 38.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) 105 min (b) 36 min (c) 3 min (d) 315 min
  39. 39.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) 5 min (b) 150 min (c) 750 min (d) 55 min
  40. 40.A teacher has 60 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 6 (c) 360 (d) 60

Answer key

  1. 80
  2. 5 cm
  3. 18 min
  4. 12 min
  5. 7 cm
  6. 10 cm
  7. 60 min
  8. 50
  9. 12 cm
  10. 5 cm
  11. 28
  12. 3 cm
  13. 126 min
  14. 9
  15. 7
  16. 42 min
  17. 75
  18. 45
  19. 8 cm
  20. 7
  21. 8
  22. 10
  23. 75 min
  24. 11
  25. 2
  26. 150
  27. 30
  28. 90 min
  29. 5
  30. 112 min
  31. 7 cm
  32. 12
  33. 10
  34. 40
  35. 18
  36. 60 min
  37. 4
  38. 105 min
  39. 150 min
  40. 12

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