HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 467 · 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 18 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 12 (c) 3 (d) 6
2. 2.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 25 (b) 60 (c) 150 (d) 30
3. 3.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) 105 (c) 315 (d) 36
4. 4.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 216 (b) 72 (c) 30 (d) 36
5. 5.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) 378 min (b) 3 min (c) 126 min (d) 39 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) 63 (b) 30 (c) 126 (d) 189
7. 7.Two ribbons are 35 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) 35 cm (c) 5 cm (d) 10 cm
8. 8.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 140 min (b) 2 min (c) 70 min (d) 24 min
9. 9.A teacher has 35 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) 35 (d) 5
10. 10.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) 84 min (b) 20 min (c) 42 min (d) 2 min
11. 11.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 45 (b) 135 (c) 24 (d) 90
12. 12.A teacher has 16 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 16 (c) 4 (d) 40
13. 13.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) 8 (b) 6 (c) 2 (d) 1
14. 14.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 120 (b) 44 (c) 480 (d) 240
15. 15.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) 180 (d) 60
16. 16.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 168 min (b) 84 min (c) 26 min (d) 2 min
17. 17.A teacher has 54 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 54 (c) 9 (d) 378
18. 18.Two ribbons are 22 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) 22 cm (b) 55 cm (c) 1 cm (d) 11 cm
19. 19.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) 252 min (c) 33 min (d) 84 min
20. 20.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) 5 min (b) 350 min (c) 45 min (d) 70 min
21. 21.Two bells ring every 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 18 min (c) 28 min (d) 56 min
22. 22.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 96 min (b) 20 min (c) 4 min (d) 24 min
23. 23.A teacher has 36 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 24 (c) 12 (d) 6
24. 24.Two ribbons are 28 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) 1 cm (b) 28 cm (c) 140 cm (d) 7 cm
25. 25.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 280 (b) 140 (c) 700 (d) 55
26. 26.A teacher has 56 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 8 (c) 56 (d) 4
27. 27.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 2 min (c) 16 min (d) 30 min
28. 28.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) 14 cm (c) 112 cm (d) 2 cm
29. 29.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) 21 cm (c) 1 cm (d) 7 cm
30. 30.A teacher has 20 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 70 (b) 5 (c) 10 (d) 20
31. 31.Two bells ring every 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 56 min (c) 22 min (d) 112 min
32. 32.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) 120 (c) 60 (d) 32
33. 33.A teacher has 22 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 33 (b) 22 (c) 1 (d) 11
34. 34.Two ribbons are 30 cm and 48 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 6 cm (b) 18 cm (c) 3 cm (d) 30 cm
35. 35.Two ribbons are 15 cm and 18 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) 90 cm
36. 36.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 70 (b) 24 (c) 71 (d) 140
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) 240 min (b) 4 min (c) 60 min (d) 32 min
38. 38.A teacher has 18 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 6 (c) 3 (d) 72
39. 39.Two bells ring every 6 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 126 min (b) 27 min (c) 42 min (d) 3 min
40. 40.A teacher has 14 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) 14 (c) 1 (d) 112

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