← HCF and LCM puzzles lesson New set →

HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 178 · 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 ribbons are 21 cm and 28 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 21 cm (b) 84 cm (c) 7 cm (d) 1 cm
  2. 2.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) 112 min (d) 44 min
  3. 3.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 42 (b) 144 (c) 72 (d) 432
  4. 4.Two ribbons are 33 cm and 88 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) 55 cm (c) 1 cm (d) 33 cm
  5. 5.A teacher has 28 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 7 (c) 1 (d) 35
  6. 6.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 30 (b) 25 (c) 150 (d) 60
  7. 7.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) 105 (d) 36
  8. 8.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 126 (b) 42 (c) 27 (d) 84
  9. 9.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) 280 (c) 140 (d) 48
  10. 10.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 180 (b) 120 (c) 27 (d) 60
  11. 11.A teacher has 20 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 8 (c) 2 (d) 4
  12. 12.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) 4 (c) 1 (d) 2
  13. 13.Two bells ring every 8 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 18 min (c) 2 min (d) 80 min
  14. 14.Two bells ring every 8 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 160 min (c) 40 min (d) 28 min
  15. 15.Two ribbons are 25 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) 1 cm (b) 5 cm (c) 20 cm (d) 25 cm
  16. 16.A teacher has 36 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 252 (c) 3 (d) 6
  17. 17.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) 40 min (c) 2 min (d) 14 min
  18. 18.Two ribbons are 14 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) 14 cm (b) 7 cm (c) 21 cm (d) 1 cm
  19. 19.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 48 (b) 24 (c) 20 (d) 96
  20. 20.Two ribbons are 63 cm and 72 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) 504 cm (c) 9 cm (d) 3 cm
  21. 21.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 43 (b) 84 (c) 20 (d) 42
  22. 22.Two ribbons are 6 cm and 9 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) 18 cm (c) 6 cm (d) 1 cm
  23. 23.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 180 (b) 33 (c) 90 (d) 270
  24. 24.Two ribbons are 12 cm and 14 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) 84 cm (c) 12 cm (d) 1 cm
  25. 25.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) 3 min (b) 36 min (c) 21 min (d) 108 min
  26. 26.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 120 (b) 300 (c) 60 (d) 35
  27. 27.A teacher has 60 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) 60 (c) 12 (d) 24
  28. 28.Two ribbons are 16 cm and 28 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) 12 cm (d) 2 cm
  29. 29.Two ribbons are 4 cm and 14 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 10 cm (b) 1 cm (c) 2 cm (d) 4 cm
  30. 30.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) 6 (b) 2 (c) 8 (d) 1
  31. 31.Two bells ring every 12 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 30 min (c) 36 min (d) 216 min
  32. 32.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) 1 cm (c) 7 cm (d) 28 cm
  33. 33.A teacher has 24 pencils and 36 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) 72
  34. 34.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) 84 (d) 33
  35. 35.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 60 (b) 21 (c) 30 (d) 90
  36. 36.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 28 (b) 192 (c) 96 (d) 48
  37. 37.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) 12 (c) 1 (d) 3
  38. 38.A teacher has 20 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 120 (b) 2 (c) 4 (d) 20
  39. 39.A teacher has 8 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 40 (c) 8 (d) 1
  40. 40.Two ribbons are 24 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) 12 cm (b) 60 cm (c) 24 cm (d) 6 cm

Answer key

  1. 7 cm
  2. 112 min
  3. 72
  4. 11 cm
  5. 7
  6. 30
  7. 105
  8. 42
  9. 140
  10. 60
  11. 4
  12. 2
  13. 40 min
  14. 40 min
  15. 5 cm
  16. 6
  17. 20 min
  18. 7 cm
  19. 24
  20. 9 cm
  21. 42
  22. 3 cm
  23. 90
  24. 2 cm
  25. 36 min
  26. 60
  27. 12
  28. 4 cm
  29. 2 cm
  30. 2
  31. 36 min
  32. 7 cm
  33. 12
  34. 84
  35. 30
  36. 48
  37. 3
  38. 4
  39. 2
  40. 12 cm

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