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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 97 · 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 20 children, with none left over? (a) 240 (b) 32 (c) 120 (d) 60
  2. 2.A teacher has 18 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 27 (c) 3 (d) 9
  3. 3.Two bells ring every 6 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 27 min (b) 126 min (c) 3 min (d) 42 min
  4. 4.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) 36 (c) 105 (d) 315
  5. 5.A teacher has 18 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 18 (c) 6 (d) 12
  6. 6.Two ribbons are 48 cm and 84 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) 48 cm (c) 12 cm (d) 36 cm
  7. 7.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) 144 (b) 6 (c) 36 (d) 12
  8. 8.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 18 (b) 80 (c) 40 (d) 41
  9. 9.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) 4 (b) 1 (c) 2 (d) 14
  10. 10.Two ribbons are 15 cm and 20 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) 15 cm (c) 60 cm (d) 1 cm
  11. 11.A teacher has 55 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) 55 (d) 22
  12. 12.Two bells ring every 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 56 min (b) 2 min (c) 112 min (d) 22 min
  13. 13.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) 84 (b) 12 (c) 6 (d) 24
  14. 14.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
  15. 15.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) 4 min (b) 448 min (c) 112 min (d) 44 min
  16. 16.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) 22 min (b) 120 min (c) 60 min (d) 2 min
  17. 17.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
  18. 18.Two ribbons are 6 cm and 16 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) 2 cm (c) 10 cm (d) 6 cm
  19. 19.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 24 (b) 48 (c) 14 (d) 25
  20. 20.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) 20 min (c) 2 min (d) 40 min
  21. 21.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 10 (b) 24 (c) 12 (d) 13
  22. 22.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) 10 min (b) 12 min (c) 2 min (d) 24 min
  23. 23.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) 3 min (b) 24 min (c) 45 min (d) 135 min
  24. 24.A teacher has 9 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
  25. 25.Two ribbons are 44 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) 33 cm (b) 1 cm (c) 11 cm (d) 44 cm
  26. 26.A teacher has 16 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 4 (c) 24 (d) 16
  27. 27.A teacher has 10 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 2 (c) 10 (d) 4
  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) 105 min (b) 5 min (c) 525 min (d) 50 min
  29. 29.A teacher has 16 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) 4 (c) 2 (d) 16
  30. 30.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 320 min (c) 80 min (d) 4 min
  31. 31.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) 350 min (d) 70 min
  32. 32.A teacher has 24 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 120 (c) 3 (d) 6
  33. 33.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) 84 min (b) 33 min (c) 3 min (d) 252 min
  34. 34.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 44 min (b) 4 min (c) 120 min (d) 480 min
  35. 35.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 432 (b) 144 (c) 42 (d) 72
  36. 36.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
  37. 37.A teacher has 72 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 72 (c) 648 (d) 9
  38. 38.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 61 (b) 120 (c) 60 (d) 22
  39. 39.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 189 min (b) 30 min (c) 3 min (d) 63 min
  40. 40.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) 44 (b) 1 (c) 11 (d) 33

Answer key

  1. 60
  2. 9
  3. 42 min
  4. 105
  5. 6
  6. 12 cm
  7. 12
  8. 40
  9. 2
  10. 5 cm
  11. 11
  12. 56 min
  13. 12
  14. 8
  15. 112 min
  16. 60 min
  17. 36
  18. 2 cm
  19. 24
  20. 20 min
  21. 12
  22. 12 min
  23. 45 min
  24. 3
  25. 11 cm
  26. 8
  27. 2
  28. 105 min
  29. 4
  30. 80 min
  31. 70 min
  32. 6
  33. 84 min
  34. 120 min
  35. 72
  36. 70 min
  37. 9
  38. 60
  39. 63 min
  40. 11

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