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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 191 · 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 8 children or among 12 children, with none left over? (a) 96 (b) 48 (c) 20 (d) 24
  2. 2.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) 315 (c) 36 (d) 210
  3. 3.A teacher has 70 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
  4. 4.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) 10 (b) 2 (c) 1 (d) 4
  5. 5.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 168 (b) 252 (c) 33 (d) 84
  6. 6.A teacher has 12 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
  7. 7.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 84 (b) 42 (c) 43 (d) 20
  8. 8.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) 11 cm (b) 1 cm (c) 44 cm (d) 33 cm
  9. 9.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 250 min (b) 5 min (c) 50 min (d) 35 min
  10. 10.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) 448 min (b) 44 min (c) 4 min (d) 112 min
  11. 11.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) 4 min (c) 320 min (d) 80 min
  12. 12.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 4 min (c) 84 min (d) 336 min
  13. 13.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) 42 min (b) 126 min (c) 3 min (d) 27 min
  14. 14.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) 2 min (c) 12 min (d) 24 min
  15. 15.A teacher has 56 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 56 (b) 448 (c) 4 (d) 8
  16. 16.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) 525 min (c) 50 min (d) 105 min
  17. 17.A teacher has 24 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 24 (c) 12 (d) 60
  18. 18.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) 60 min (b) 240 min (c) 4 min (d) 32 min
  19. 19.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) 140 min (b) 4 min (c) 48 min (d) 560 min
  20. 20.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 84 min (c) 26 min (d) 168 min
  21. 21.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) 3 cm (b) 12 cm (c) 42 cm (d) 6 cm
  22. 22.A teacher has 9 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 12 (d) 1
  23. 23.Two ribbons are 16 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) 16 cm (b) 4 cm (c) 8 cm (d) 48 cm
  24. 24.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 280 (b) 560 (c) 48 (d) 140
  25. 25.A teacher has 22 pencils and 55 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) 33 (d) 11
  26. 26.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) 2 cm (b) 4 cm (c) 6 cm (d) 1 cm
  27. 27.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) 10 (b) 2 (c) 1 (d) 8
  28. 28.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) 20 min (b) 42 min (c) 84 min (d) 2 min
  29. 29.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) 41 (c) 80 (d) 40
  30. 30.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) 3 min (b) 126 min (c) 378 min (d) 39 min
  31. 31.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) 60 (d) 61
  32. 32.A teacher has 55 pencils and 66 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 330 (b) 11 (c) 1 (d) 55
  33. 33.Two ribbons are 48 cm and 108 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) 60 cm (c) 48 cm (d) 12 cm
  34. 34.A teacher has 36 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 9 (c) 36 (d) 180
  35. 35.A teacher has 48 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 48 (c) 12 (d) 6
  36. 36.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) 5 (c) 30 (d) 10
  37. 37.A teacher has 12 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 4 (c) 2 (d) 48
  38. 38.A teacher has 44 pencils and 99 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) 44
  39. 39.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 120 min (b) 6 min (c) 54 min (d) 720 min
  40. 40.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) 14 (c) 25 (d) 48

Answer key

  1. 24
  2. 105
  3. 10
  4. 2
  5. 84
  6. 6
  7. 42
  8. 11 cm
  9. 50 min
  10. 112 min
  11. 80 min
  12. 84 min
  13. 42 min
  14. 12 min
  15. 8
  16. 105 min
  17. 12
  18. 60 min
  19. 140 min
  20. 84 min
  21. 6 cm
  22. 3
  23. 8 cm
  24. 140
  25. 11
  26. 2 cm
  27. 2
  28. 42 min
  29. 40
  30. 126 min
  31. 60
  32. 11
  33. 12 cm
  34. 9
  35. 12
  36. 10
  37. 4
  38. 11
  39. 120 min
  40. 24

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