HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 762 · 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 8 children or among 28 children, with none left over? (a) 112 (b) 224 (c) 56 (d) 36
2. 2.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) 4 cm (b) 20 cm (c) 120 cm (d) 2 cm
3. 3.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) 2 min (b) 80 min (c) 40 min (d) 18 min
4. 4.Two ribbons are 45 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) 9 cm (b) 3 cm (c) 270 cm (d) 45 cm
5. 5.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) 8 (d) 56
6. 6.A teacher has 27 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 27 (b) 9 (c) 3 (d) 36
7. 7.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) 432 min (b) 42 min (c) 6 min (d) 72 min
8. 8.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 44 min (b) 120 min (c) 4 min (d) 480 min
9. 9.A teacher has 21 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 168 (b) 1 (c) 21 (d) 3
10. 10.Two ribbons are 56 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) 4 cm (b) 16 cm (c) 8 cm (d) 56 cm
11. 11.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) 4 (d) 20
12. 12.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 21 (b) 30 (c) 90 (d) 60
13. 13.Two ribbons are 6 cm and 8 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) 6 cm (c) 2 cm (d) 1 cm
14. 14.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) 21 min (c) 3 min (d) 90 min
15. 15.Two ribbons are 18 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) 126 cm (b) 3 cm (c) 1 cm (d) 18 cm
16. 16.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 750 min (b) 5 min (c) 55 min (d) 150 min
17. 17.A teacher has 14 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 1 (c) 7 (d) 21
18. 18.A teacher has 32 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 8 (c) 4 (d) 32
19. 19.A teacher has 40 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 24 (c) 4 (d) 40
20. 20.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) 16 (d) 4
21. 21.A teacher has 20 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 5 (c) 10 (d) 60
22. 22.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) 4 min (c) 84 min (d) 336 min
23. 23.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 35 (b) 120 (c) 60 (d) 300
24. 24.Two bells ring every 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 90 min (c) 48 min (d) 540 min
25. 25.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 350 min (b) 5 min (c) 70 min (d) 45 min
26. 26.Two ribbons are 55 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) 33 cm (b) 11 cm (c) 55 cm (d) 1 cm
27. 27.Two ribbons are 4 cm and 6 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) 12 cm (c) 1 cm (d) 4 cm
28. 28.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) 5 min (b) 105 min (c) 525 min (d) 50 min
29. 29.Two ribbons are 28 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
30. 30.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 40 min (c) 75 min (d) 375 min
31. 31.A teacher has 6 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) 6 (c) 1 (d) 4
32. 32.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 105 min (c) 315 min (d) 36 min
33. 33.A teacher has 36 pencils and 81 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) 45 (d) 36
34. 34.A teacher has 63 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 63 (c) 3 (d) 9
35. 35.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) 45 min (b) 500 min (c) 5 min (d) 100 min
36. 36.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) 24 (b) 1 (c) 2 (d) 6
37. 37.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) 60 min (b) 4 min (c) 32 min (d) 240 min
38. 38.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 28 (b) 80 (c) 160 (d) 40
39. 39.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 55 (b) 280 (c) 700 (d) 140
40. 40.A teacher has 28 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 224 (b) 28 (c) 2 (d) 4

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