HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 841 · 40 questions

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.

1. 1.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) 4 min (b) 32 min (c) 60 min (d) 240 min
2. 2.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) 12 (b) 18 (c) 3 (d) 6
3. 3.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) 15 min (b) 18 min (c) 3 min (d) 54 min
4. 4.Two ribbons are 12 cm and 20 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) 8 cm (c) 4 cm (d) 2 cm
5. 5.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
6. 6.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) 33 (b) 1 (c) 132 (d) 11
7. 7.A teacher has 60 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 12 (c) 60 (d) 6
8. 8.Two ribbons are 15 cm and 25 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) 5 cm (c) 1 cm (d) 10 cm
9. 9.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) 3 cm (b) 18 cm (c) 63 cm (d) 9 cm
10. 10.Two ribbons are 14 cm and 16 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) 2 cm (c) 112 cm (d) 14 cm
11. 11.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) 80 min (c) 2 min (d) 18 min
12. 12.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 90 (c) 45 (d) 135
13. 13.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) 4 min (c) 192 min (d) 48 min
14. 14.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) 10 (b) 1 (c) 5 (d) 35
15. 15.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 140 (b) 700 (c) 55 (d) 280
16. 16.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
17. 17.A teacher has 77 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) 77 (c) 1 (d) 22
18. 18.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 700 min (b) 140 min (c) 55 min (d) 5 min
19. 19.A teacher has 33 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 33 (c) 44 (d) 1
20. 20.A teacher has 12 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 60 (c) 1 (d) 12
21. 21.A teacher has 24 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 6 (c) 3 (d) 120
22. 22.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) 1 cm (b) 21 cm (c) 7 cm (d) 84 cm
23. 23.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) 21 cm (b) 1 cm (c) 3 cm (d) 6 cm
24. 24.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) 1 cm (d) 7 cm
25. 25.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
26. 26.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) 48 (c) 140 (d) 560
27. 27.Two ribbons are 72 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) 648 cm (b) 9 cm (c) 3 cm (d) 72 cm
28. 28.Two ribbons are 8 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) 8 cm (c) 1 cm (d) 6 cm
29. 29.Two ribbons are 20 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) 4 cm (b) 20 cm (c) 2 cm (d) 16 cm
30. 30.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) 30 (c) 90 (d) 21
31. 31.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 350 (b) 45 (c) 70 (d) 140
32. 32.A teacher has 18 pencils and 42 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) 24
33. 33.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) 72 min (c) 42 min (d) 432 min
34. 34.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) 96 (c) 192 (d) 48
35. 35.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) 2 (b) 20 (c) 4 (d) 16
36. 36.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) 61 (c) 60 (d) 22
37. 37.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) 24 (b) 216 (c) 1 (d) 3
38. 38.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 27 (b) 120 (c) 60 (d) 180
39. 39.A teacher has 10 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) 10 (c) 1 (d) 6
40. 40.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) 4 min (b) 320 min (c) 36 min (d) 80 min

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