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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 810 · 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.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) 30 (b) 3 (c) 12 (d) 6
  2. 2.Two bells ring every 8 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 40 min (c) 28 min (d) 160 min
  3. 3.A teacher has 10 pencils and 25 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) 5 (d) 10
  4. 4.Two ribbons are 15 cm and 25 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) 1 cm (d) 15 cm
  5. 5.Two ribbons are 12 cm and 14 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 84 cm (b) 1 cm (c) 2 cm (d) 12 cm
  6. 6.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) 12 (b) 15 (c) 3 (d) 1
  7. 7.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) 18 (c) 56 (d) 28
  8. 8.Two ribbons are 50 cm and 80 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 50 cm (b) 10 cm (c) 30 cm (d) 5 cm
  9. 9.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
  10. 10.Two ribbons are 55 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) 55 cm (b) 33 cm (c) 11 cm (d) 1 cm
  11. 11.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) 6 (b) 12 (c) 144 (d) 36
  12. 12.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 168 (b) 336 (c) 40 (d) 84
  13. 13.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) 18 min (c) 2 min (d) 28 min
  14. 14.Two ribbons are 22 cm and 77 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 22 cm (b) 11 cm (c) 55 cm (d) 1 cm
  15. 15.Two ribbons are 48 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 432 cm (b) 48 cm (c) 6 cm (d) 3 cm
  16. 16.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) 6 min (c) 60 min (d) 360 min
  17. 17.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) 7 (b) 14 (c) 21 (d) 1
  18. 18.Two ribbons are 42 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 42 cm (b) 12 cm (c) 6 cm (d) 3 cm
  19. 19.Two ribbons are 24 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 24 cm (b) 30 cm (c) 6 cm (d) 3 cm
  20. 20.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 42 (b) 84 (c) 43 (d) 20
  21. 21.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
  22. 22.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) 9 cm (c) 54 cm (d) 18 cm
  23. 23.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 200 (b) 100 (c) 45 (d) 500
  24. 24.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 45 (c) 90 (d) 135
  25. 25.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 54 (b) 84 (c) 168 (d) 504
  26. 26.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 27 (b) 180 (c) 60 (d) 120
  27. 27.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) 40 min (b) 2 min (c) 20 min (d) 14 min
  28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 60 (b) 240 (c) 32 (d) 120
  29. 29.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 100 (b) 250 (c) 35 (d) 50
  30. 30.Two bells ring every 6 minutes and every 8 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 48 min (c) 14 min (d) 24 min
  31. 31.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 105 (b) 36 (c) 210 (d) 315
  32. 32.Two ribbons are 6 cm and 9 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) 6 cm (c) 3 cm (d) 1 cm
  33. 33.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
  34. 34.A teacher has 40 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 40 (c) 30 (d) 5
  35. 35.Two ribbons are 4 cm and 10 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) 1 cm (c) 2 cm (d) 6 cm
  36. 36.A teacher has 33 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) 33 (c) 44 (d) 11
  37. 37.A teacher has 8 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 2 (c) 8 (d) 4
  38. 38.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) 6 min (b) 48 min (c) 90 min (d) 540 min
  39. 39.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 15 (b) 18 (c) 36 (d) 54
  40. 40.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) 180 min (b) 27 min (c) 3 min (d) 60 min

Answer key

  1. 6
  2. 40 min
  3. 5
  4. 5 cm
  5. 2 cm
  6. 3
  7. 28
  8. 10 cm
  9. 105 min
  10. 11 cm
  11. 12
  12. 84
  13. 28 min
  14. 11 cm
  15. 6 cm
  16. 60 min
  17. 7
  18. 6 cm
  19. 6 cm
  20. 42
  21. 2
  22. 9 cm
  23. 100
  24. 45
  25. 84
  26. 60
  27. 20 min
  28. 60
  29. 50
  30. 24 min
  31. 105
  32. 3 cm
  33. 90
  34. 10
  35. 2 cm
  36. 11
  37. 4
  38. 90 min
  39. 18
  40. 60 min

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