HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 648 · 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.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) 2 (b) 168 (c) 24 (d) 4
2. 2.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 28 (b) 29 (c) 56 (d) 18
3. 3.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 224 (b) 44 (c) 112 (d) 448
4. 4.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) 12 (b) 6 (c) 60 (d) 48
5. 5.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) 4 min (d) 48 min
6. 6.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 126 (b) 63 (c) 189 (d) 30
7. 7.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 112 (b) 56 (c) 22 (d) 57
8. 8.Two ribbons are 35 cm and 49 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) 1 cm (c) 35 cm (d) 14 cm
9. 9.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) 1 cm (b) 8 cm (c) 2 cm (d) 6 cm
10. 10.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) 432 (d) 72
11. 11.Two ribbons are 10 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) 1 cm (b) 10 cm (c) 5 cm (d) 30 cm
12. 12.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 70 (b) 140 (c) 45 (d) 350
13. 13.Two ribbons are 21 cm and 49 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 28 cm (b) 1 cm (c) 21 cm (d) 7 cm
14. 14.A teacher has 48 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 36 (c) 6 (d) 48
15. 15.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 18 (c) 54 (d) 15
16. 16.Two ribbons are 15 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) 1 cm (b) 3 cm (c) 15 cm (d) 6 cm
17. 17.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) 45 (c) 90 (d) 135
18. 18.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 39 (b) 126 (c) 378 (d) 252
19. 19.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 22 min (c) 2 min (d) 120 min
20. 20.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) 63 min (b) 3 min (c) 30 min (d) 189 min
21. 21.A teacher has 9 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 1 (d) 6
22. 22.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) 60 min (c) 6 min (d) 756 min
23. 23.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) 36 min (b) 6 min (c) 216 min (d) 30 min
24. 24.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) 10 cm (b) 15 cm (c) 5 cm (d) 1 cm
25. 25.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 35 min (c) 50 min (d) 250 min
26. 26.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) 4 min (c) 80 min (d) 36 min
27. 27.A teacher has 25 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 1 (c) 20 (d) 25
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 240 (b) 60 (c) 120 (d) 32
29. 29.A teacher has 21 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 84 (c) 1 (d) 7
30. 30.A teacher has 10 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) 2 (c) 8 (d) 10
31. 31.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) 14 (b) 7 (c) 42 (d) 1
32. 32.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) 140 min (b) 700 min (c) 5 min (d) 55 min
33. 33.Two ribbons are 45 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) 18 cm (b) 9 cm (c) 3 cm (d) 45 cm
34. 34.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 120 (b) 27 (c) 180 (d) 60
35. 35.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 84 min (c) 252 min (d) 33 min
36. 36.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) 14 min (b) 2 min (c) 24 min (d) 48 min
37. 37.A teacher has 22 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 1 (c) 22 (d) 11
38. 38.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 336 min (c) 84 min (d) 4 min
39. 39.Two ribbons are 20 cm and 24 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 120 cm (b) 2 cm (c) 20 cm (d) 4 cm
40. 40.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) 5 min (c) 50 min (d) 105 min

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