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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 139 · 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.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) 48 min (b) 140 min (c) 4 min (d) 560 min
  2. 2.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 525 (b) 210 (c) 105 (d) 50
  3. 3.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 750 (b) 300 (c) 55 (d) 150
  4. 4.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 36 (b) 80 (c) 160 (d) 320
  5. 5.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 378 (b) 252 (c) 39 (d) 126
  6. 6.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) 350 min (b) 45 min (c) 5 min (d) 70 min
  7. 7.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 84 (b) 252 (c) 168 (d) 33
  8. 8.A teacher has 15 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
  9. 9.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 120 (b) 54 (c) 240 (d) 720
  10. 10.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) 320 min (b) 80 min (c) 36 min (d) 4 min
  11. 11.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 18 (b) 15 (c) 54 (d) 36
  12. 12.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 140 (b) 71 (c) 70 (d) 24
  13. 13.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 224 min (c) 56 min (d) 4 min
  14. 14.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) 54 min (c) 18 min (d) 15 min
  15. 15.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 560 (b) 48 (c) 140 (d) 280
  16. 16.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) 28 min (b) 56 min (c) 18 min (d) 2 min
  17. 17.A teacher has 36 pencils and 60 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) 24 (d) 36
  18. 18.A teacher has 9 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 1 (c) 6 (d) 3
  19. 19.Two bells ring every 12 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 54 min (c) 84 min (d) 504 min
  20. 20.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 112 (b) 56 (c) 57 (d) 22
  21. 21.Two ribbons are 35 cm and 63 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) 28 cm (c) 7 cm (d) 1 cm
  22. 22.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 90 (b) 21 (c) 30 (d) 60
  23. 23.A teacher has 21 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 21 (c) 168 (d) 3
  24. 24.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) 14 min (b) 2 min (c) 48 min (d) 24 min
  25. 25.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) 4 min (c) 44 min (d) 112 min
  26. 26.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) 12 (b) 36 (c) 6 (d) 144
  27. 27.A teacher has 42 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 42 (c) 6 (d) 12
  28. 28.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 28 (b) 29 (c) 56 (d) 18
  29. 29.A teacher has 27 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 27 (b) 9 (c) 3 (d) 36
  30. 30.Two ribbons are 28 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) 2 cm (b) 4 cm (c) 8 cm (d) 28 cm
  31. 31.A teacher has 22 pencils and 33 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 66 (b) 1 (c) 22 (d) 11
  32. 32.A teacher has 10 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 1 (c) 5 (d) 10
  33. 33.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) 525 min (b) 105 min (c) 5 min (d) 50 min
  34. 34.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) 3 (b) 6 (c) 72 (d) 18
  35. 35.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) 30 (b) 10 (c) 40 (d) 5
  36. 36.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) 2 (b) 48 (c) 4 (d) 12
  37. 37.A teacher has 33 pencils and 44 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 132 (b) 11 (c) 33 (d) 1
  38. 38.Two ribbons are 14 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) 42 cm (b) 14 cm (c) 7 cm (d) 1 cm
  39. 39.A teacher has 24 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 6 (c) 24 (d) 30
  40. 40.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 85 (b) 26 (c) 168 (d) 84

Answer key

  1. 140 min
  2. 105
  3. 150
  4. 80
  5. 126
  6. 70 min
  7. 84
  8. 3
  9. 120
  10. 80 min
  11. 18
  12. 70
  13. 56 min
  14. 18 min
  15. 140
  16. 28 min
  17. 12
  18. 3
  19. 84 min
  20. 56
  21. 7 cm
  22. 30
  23. 3
  24. 24 min
  25. 112 min
  26. 12
  27. 6
  28. 28
  29. 9
  30. 4 cm
  31. 11
  32. 5
  33. 105 min
  34. 6
  35. 10
  36. 4
  37. 11
  38. 7 cm
  39. 6
  40. 84

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