HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 625 · 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.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) 50 (c) 210 (d) 105
2. 2.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 63 (b) 30 (c) 189 (d) 126
3. 3.A teacher has 35 pencils and 56 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) 35 (d) 7
4. 4.Two ribbons are 16 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) 16 cm (c) 20 cm (d) 4 cm
5. 5.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) 30 min (b) 3 min (c) 21 min (d) 90 min
6. 6.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) 216 min (b) 36 min (c) 30 min (d) 6 min
7. 7.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 252 (b) 126 (c) 378 (d) 39
8. 8.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 60 (b) 252 (c) 126 (d) 756
9. 9.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) 5 min (b) 25 min (c) 30 min (d) 150 min
10. 10.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) 240 min (c) 32 min (d) 60 min
11. 11.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) 320 (c) 80 (d) 160
12. 12.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 25 (b) 14 (c) 48 (d) 24
13. 13.A teacher has 18 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 126 (b) 1 (c) 3 (d) 18
14. 14.A teacher has 6 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 10 (c) 2 (d) 1
15. 15.A teacher has 45 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) 45 (c) 9 (d) 270
16. 16.A teacher has 50 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 300 (c) 50 (d) 10
17. 17.Two ribbons are 84 cm and 96 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 84 cm (b) 672 cm (c) 6 cm (d) 12 cm
18. 18.A teacher has 20 pencils and 50 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) 5 (d) 20
19. 19.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) 3 min (c) 30 min (d) 63 min
20. 20.A teacher has 32 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 32 (b) 4 (c) 288 (d) 2
21. 21.Two ribbons are 12 cm and 15 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) 60 cm (c) 1 cm (d) 12 cm
22. 22.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) 8 cm (b) 28 cm (c) 4 cm (d) 2 cm
23. 23.A teacher has 14 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 49 (b) 7 (c) 1 (d) 14
24. 24.A teacher has 12 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 30 (c) 6 (d) 12
25. 25.A teacher has 48 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 336 (c) 4 (d) 8
26. 26.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 33 (b) 84 (c) 252 (d) 168
27. 27.A teacher has 8 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 8 (c) 20 (d) 4
28. 28.Two ribbons are 35 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) 7 cm (b) 35 cm (c) 21 cm (d) 1 cm
29. 29.A teacher has 6 pencils and 9 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 1 (c) 18 (d) 3
30. 30.Two ribbons are 66 cm and 77 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 66 cm (b) 462 cm (c) 1 cm (d) 11 cm
31. 31.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 100 min (b) 45 min (c) 5 min (d) 500 min
32. 32.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) 224 min (c) 4 min (d) 36 min
33. 33.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 57 (b) 22 (c) 112 (d) 56
34. 34.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 10 min (c) 12 min (d) 24 min
35. 35.A teacher has 6 pencils and 8 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 6 (c) 24 (d) 2
36. 36.Two ribbons are 21 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) 21 cm (b) 1 cm (c) 7 cm (d) 35 cm
37. 37.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 60 (b) 120 (c) 360 (d) 42
38. 38.Two ribbons are 24 cm and 40 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) 24 cm (d) 8 cm
39. 39.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) 12 cm (b) 2 cm (c) 1 cm (d) 84 cm
40. 40.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) 21 cm (b) 7 cm (c) 14 cm (d) 1 cm

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