HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 418 · 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.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
2. 2.Three temple bells ring every 8, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
3. 3.Arjun takes 36 seconds and Manav 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?
4. 4.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
5. 5.Three temple bells ring every 8, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
6. 6.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 8.
7. 7.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 8.
8. 8.Two tanks hold 75 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
9. 9.Rahul takes 75 seconds and Karan 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?
10. 10.Ishaan takes 45 seconds and Aditya takes 60 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?
11. 11.Three temple bells ring every 20, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
12. 12.Two tanks hold 120 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
13. 13.Three temple bells ring every 30, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
14. 14.A hall floor is 315 cm long and 225 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 15 that leaves a remainder of 2 when divided by 10, 3 or 15.
16. 16.Three temple bells ring every 8, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
17. 17.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 5.
18. 18.Three temple bells ring every 4, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
19. 19.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?
20. 20.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 5 or 3.
21. 21.Three temple bells ring every 6, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
22. 22.Three temple bells ring every 18, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.Three temple bells ring every 10, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
24. 24.Two tanks hold 30 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
25. 25.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 3 or 6.
26. 26.Two tanks hold 90 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
27. 27.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
28. 28.Three temple bells ring every 12, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
29. 29.Three temple bells ring every 4, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
30. 30.Three temple bells ring every 6, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
31. 31.Two tanks hold 210 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
32. 32.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 6, 10 or 4.
33. 33.Two tanks hold 80 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
34. 34.Three temple bells ring every 8, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 12 or 3.
36. 36.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 8 or 5.
37. 37.Three temple bells ring every 10, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
38. 38.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 8 or 15.
39. 39.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
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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