HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 294 · 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.Aarav takes 30 seconds and Rahul takes 50 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?
2. 2.Three temple bells ring every 12, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
3. 3.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 8, 10 or 6.
4. 4.Two tanks hold 300 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
5. 5.Two tanks hold 20 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
6. 6.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?
7. 7.Two tanks hold 150 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
8. 8.Two tanks hold 90 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
9. 9.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 6 or 9.
10. 10.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 6 or 3.
11. 11.Rohan takes 48 seconds and Nisha takes 36 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?
12. 12.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 4.
13. 13.Three temple bells ring every 12, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
14. 14.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 12, 9 or 15.
15. 15.Farhan takes 30 seconds and Aarav 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?
16. 16.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 6, 3 or 4.
17. 17.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 10.
18. 18.Dev takes 50 seconds and Rahul takes 90 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 45 litres and 60 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 405 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
21. 21.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 5 or 8.
22. 22.Three temple bells ring every 15, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
24. 24.Two tanks hold 40 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
25. 25.Three temple bells ring every 5, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
26. 26.Two tanks hold 105 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
27. 27.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 6.
28. 28.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 6 or 9.
29. 29.Two tanks hold 160 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
30. 30.Two tanks hold 15 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
31. 31.Isha takes 36 seconds and Nisha takes 90 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 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
33. 33.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 3.
34. 34.Three temple bells ring every 6, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
36. 36.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
37. 37.Three temple bells ring every 20, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
38. 38.Three temple bells ring every 4, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.Two tanks hold 320 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
40. 40.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

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