← HCF and LCM puzzles lesson New set →

HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 49 · 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 6 children or among 21 children, with none left over? (a) 27 (b) 42 (c) 126 (d) 84
  2. 2.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) 560 min (b) 4 min (c) 48 min (d) 140 min
  3. 3.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) 20 (c) 48 (d) 24
  4. 4.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) 24 min (b) 135 min (c) 45 min (d) 3 min
  5. 5.Two ribbons are 30 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) 3 cm (c) 6 cm (d) 30 cm
  6. 6.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) 20 min (b) 14 min (c) 2 min (d) 40 min
  7. 7.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
  8. 8.A teacher has 49 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 49 (b) 392 (c) 1 (d) 7
  9. 9.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 24 (c) 10 (d) 13
  10. 10.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) 48 (d) 2
  11. 11.Two ribbons are 6 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) 21 cm (c) 6 cm (d) 1 cm
  12. 12.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) 3 min (b) 189 min (c) 63 min (d) 30 min
  13. 13.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) 50 (d) 105
  14. 14.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 80 (b) 28 (c) 160 (d) 40
  15. 15.Two ribbons are 18 cm and 81 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 63 cm (b) 9 cm (c) 3 cm (d) 18 cm
  16. 16.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 28 min (b) 192 min (c) 48 min (d) 4 min
  17. 17.A teacher has 12 pencils and 30 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) 18 (d) 12
  18. 18.A teacher has 24 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 216 (c) 24 (d) 3
  19. 19.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) 240 min (b) 32 min (c) 60 min (d) 4 min
  20. 20.Two ribbons are 24 cm and 56 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) 8 cm (c) 4 cm (d) 32 cm
  21. 21.A teacher has 24 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 168 (b) 4 (c) 24 (d) 2
  22. 22.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) 4 (b) 448 (c) 56 (d) 8
  23. 23.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 60 (b) 25 (c) 150 (d) 30
  24. 24.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 45 (b) 140 (c) 70 (d) 350
  25. 25.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 112 (b) 56 (c) 36 (d) 224
  26. 26.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) 25 (c) 48 (d) 14
  27. 27.A teacher has 21 pencils and 56 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) 21 (d) 7
  28. 28.Two ribbons are 12 cm and 42 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 30 cm (b) 12 cm (c) 6 cm (d) 3 cm
  29. 29.A teacher has 50 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 10 (c) 5 (d) 50
  30. 30.A teacher has 40 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 240 (b) 8 (c) 4 (d) 40
  31. 31.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) 16 (b) 4 (c) 20 (d) 2
  32. 32.A teacher has 12 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 6 (c) 36 (d) 3
  33. 33.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) 18 min (b) 56 min (c) 28 min (d) 2 min
  34. 34.A teacher has 15 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) 15 (c) 1 (d) 9
  35. 35.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 18 (b) 56 (c) 29 (d) 28
  36. 36.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 85 (c) 84 (d) 168
  37. 37.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 21 min (b) 3 min (c) 90 min (d) 30 min
  38. 38.Two ribbons are 49 cm and 56 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 49 cm (b) 1 cm (c) 392 cm (d) 7 cm
  39. 39.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 112 (b) 448 (c) 44 (d) 224
  40. 40.A teacher has 6 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 2 (c) 6 (d) 1

Answer key

  1. 42
  2. 140 min
  3. 24
  4. 45 min
  5. 6 cm
  6. 20 min
  7. 42 min
  8. 7
  9. 12
  10. 4
  11. 3 cm
  12. 63 min
  13. 105
  14. 40
  15. 9 cm
  16. 48 min
  17. 6
  18. 3
  19. 60 min
  20. 8 cm
  21. 4
  22. 8
  23. 30
  24. 70
  25. 56
  26. 24
  27. 7
  28. 6 cm
  29. 10
  30. 8
  31. 4
  32. 6
  33. 28 min
  34. 3
  35. 28
  36. 84
  37. 30 min
  38. 7 cm
  39. 112
  40. 2

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad