HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 517 · 40 questions

The method (LCM or HCF?): Bells, lights, runners “together again”: find the LCM of the gaps. Biggest can, rope piece or tile that fits exactly: find the HCF. Leaves the same remainder r every time: LCM + r. Number of tiles = (length ÷ tile side) × (width ÷ tile side).

1. 1.Three temple bells ring every 4, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
2. 2.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 12, 6 or 8.
3. 3.Two tanks hold 225 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
4. 4.Two tanks hold 360 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
5. 5.Ishaan takes 72 seconds and Kabir takes 30 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
6. 6.Three temple bells ring every 20, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
7. 7.Three temple bells ring every 6, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
8. 8.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 6, 12 or 3.
9. 9.Find the smallest number bigger than 15 that leaves a remainder of 9 when divided by 15, 10 or 12.
10. 10.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
11. 11.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
12. 12.Three temple bells ring every 6, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
13. 13.Three temple bells ring every 10, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
14. 14.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
15. 15.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 6, 5 or 12.
16. 16.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
17. 17.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
18. 18.Pooja takes 75 seconds and Tara takes 30 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
19. 19.Two tanks hold 60 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
20. 20.Two tanks hold 160 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
21. 21.Two tanks hold 25 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
22. 22.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
23. 23.Three temple bells ring every 20, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
24. 24.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 10 or 6.
25. 25.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 5 or 4.
26. 26.Three temple bells ring every 5, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
27. 27.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 12 or 10.
28. 28.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 9 or 8.
29. 29.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 4 or 12.
30. 30.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 8 or 4.
31. 31.Rohan takes 45 seconds and Ananya takes 54 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
32. 32.Two tanks hold 35 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
33. 33.Two tanks hold 45 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
34. 34.Rohan takes 60 seconds and Arjun takes 45 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
35. 35.Three temple bells ring every 18, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
36. 36.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 4.
37. 37.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 4.
38. 38.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
39. 39.Three temple bells ring every 8, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
40. 40.Three temple bells ring every 30, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

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