HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 195 · 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 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 24 min (c) 3 min (d) 135 min
2. 2.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) 36 (b) 3 (c) 9 (d) 45
3. 3.A teacher has 16 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 2 (c) 4 (d) 16
4. 4.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 144 (b) 72 (c) 42 (d) 432
5. 5.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) 35 min (b) 250 min (c) 50 min (d) 5 min
6. 6.Two ribbons are 30 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) 30 cm (b) 10 cm (c) 120 cm (d) 5 cm
7. 7.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) 40 (b) 24 (c) 4 (d) 8
8. 8.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) 80 min (b) 2 min (c) 40 min (d) 18 min
9. 9.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) 10 (b) 1 (c) 2 (d) 6
10. 10.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) 45 min (c) 70 min (d) 5 min
11. 11.Two ribbons are 70 cm and 80 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 5 cm (b) 70 cm (c) 10 cm (d) 560 cm
12. 12.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) 21 min (b) 30 min (c) 3 min (d) 90 min
13. 13.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) 7 cm (b) 1 cm (c) 35 cm (d) 21 cm
14. 14.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) 2 min (b) 140 min (c) 70 min (d) 24 min
15. 15.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 10 (b) 24 (c) 12 (d) 13
16. 16.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 160 (b) 40 (c) 80 (d) 28
17. 17.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) 126 min (c) 39 min (d) 3 min
18. 18.Two ribbons are 24 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) 4 cm (b) 168 cm (c) 2 cm (d) 24 cm
19. 19.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 14 (b) 24 (c) 25 (d) 48
20. 20.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
21. 21.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) 4 (b) 224 (c) 28 (d) 2
22. 22.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) 18 (b) 3 (c) 24 (d) 6
23. 23.Two ribbons are 12 cm and 42 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) 12 cm (c) 30 cm (d) 3 cm
24. 24.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 27 (b) 42 (c) 84 (d) 126
25. 25.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) 6 min (c) 42 min (d) 72 min
26. 26.A teacher has 9 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 3 (c) 15 (d) 9
27. 27.A teacher has 60 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 420 (c) 5 (d) 10
28. 28.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) 63 min (d) 30 min
29. 29.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 140 (b) 560 (c) 280 (d) 48
30. 30.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) 252 min (b) 3 min (c) 84 min (d) 33 min
31. 31.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) 36 (b) 48 (c) 6 (d) 12
32. 32.A teacher has 30 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 180 (b) 3 (c) 6 (d) 30
33. 33.Two ribbons are 40 cm and 50 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 5 cm (b) 40 cm (c) 200 cm (d) 10 cm
34. 34.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) 126 (c) 189 (d) 30
35. 35.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) 3 cm (c) 18 cm (d) 30 cm
36. 36.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 48 (b) 192 (c) 28 (d) 96
37. 37.Two ribbons are 55 cm and 99 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 44 cm (b) 1 cm (c) 55 cm (d) 11 cm
38. 38.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 14 (b) 21 (c) 40 (d) 20
39. 39.Two ribbons are 35 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) 35 cm (b) 28 cm (c) 7 cm (d) 1 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) 105 min (b) 5 min (c) 525 min (d) 50 min

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad