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HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 769 · 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 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) 50 min (c) 5 min (d) 105 min
  2. 2.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 70 (b) 24 (c) 140 (d) 71
  3. 3.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 54 (b) 720 (c) 120 (d) 240
  4. 4.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 700 (b) 55 (c) 280 (d) 140
  5. 5.Two ribbons are 15 cm and 35 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 15 cm (b) 1 cm (c) 20 cm (d) 5 cm
  6. 6.Two ribbons are 20 cm and 45 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) 1 cm (c) 25 cm (d) 20 cm
  7. 7.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) 42 (b) 3 (c) 6 (d) 12
  8. 8.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) 3 min (b) 126 min (c) 27 min (d) 42 min
  9. 9.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) 2 min (c) 140 min (d) 70 min
  10. 10.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) 126 min (b) 378 min (c) 3 min (d) 39 min
  11. 11.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) 90 min (b) 540 min (c) 6 min (d) 48 min
  12. 12.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 14 (b) 21 (c) 40 (d) 20
  13. 13.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) 40 min (b) 375 min (c) 5 min (d) 75 min
  14. 14.A teacher has 8 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 10 (c) 2 (d) 8
  15. 15.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) 42 (c) 72 (d) 144
  16. 16.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) 126 min (b) 756 min (c) 60 min (d) 6 min
  17. 17.A teacher has 35 pencils and 49 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) 7 (d) 14
  18. 18.Two ribbons are 21 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) 6 cm (c) 1 cm (d) 21 cm
  19. 19.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 150 (b) 60 (c) 30 (d) 25
  20. 20.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 30 min (b) 5 min (c) 150 min (d) 25 min
  21. 21.Two ribbons are 54 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) 3 cm (b) 54 cm (c) 9 cm (d) 378 cm
  22. 22.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) 45 min (c) 135 min (d) 24 min
  23. 23.A teacher has 48 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 48 (c) 12 (d) 60
  24. 24.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) 6 min (b) 42 min (c) 360 min (d) 60 min
  25. 25.Two ribbons are 50 cm and 90 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) 40 cm (c) 10 cm (d) 50 cm
  26. 26.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 500 (b) 200 (c) 45 (d) 100
  27. 27.A teacher has 14 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 42 (c) 1 (d) 14
  28. 28.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) 36 min (c) 4 min (d) 80 min
  29. 29.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) 24 min (b) 48 min (c) 14 min (d) 2 min
  30. 30.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 432 min (c) 72 min (d) 42 min
  31. 31.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) 2 min (d) 18 min
  32. 32.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) 315 (c) 36 (d) 105
  33. 33.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 48 (b) 140 (c) 280 (d) 560
  34. 34.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 41 (b) 40 (c) 18 (d) 80
  35. 35.Two bells ring every 9 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 108 min (c) 21 min (d) 3 min
  36. 36.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) 56 min (b) 4 min (c) 36 min (d) 224 min
  37. 37.A teacher has 6 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 15 (c) 1 (d) 6
  38. 38.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) 63 min (c) 3 min (d) 30 min
  39. 39.A teacher has 4 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 4 (c) 6 (d) 2
  40. 40.A teacher has 15 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 3 (c) 1 (d) 15

Answer key

  1. 105 min
  2. 70
  3. 120
  4. 140
  5. 5 cm
  6. 5 cm
  7. 6
  8. 42 min
  9. 70 min
  10. 126 min
  11. 90 min
  12. 20
  13. 75 min
  14. 2
  15. 72
  16. 126 min
  17. 7
  18. 3 cm
  19. 30
  20. 30 min
  21. 9 cm
  22. 45 min
  23. 12
  24. 60 min
  25. 10 cm
  26. 100
  27. 7
  28. 80 min
  29. 24 min
  30. 72 min
  31. 28 min
  32. 105
  33. 140
  34. 40
  35. 36 min
  36. 56 min
  37. 3
  38. 63 min
  39. 2
  40. 3

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