HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 79 · 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 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
2. 2.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
3. 3.Three temple bells ring every 6, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
4. 4.Three temple bells ring every 24, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
5. 5.Two tanks hold 240 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
6. 6.Three temple bells ring every 5, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
7. 7.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?
8. 8.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
9. 9.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?
10. 10.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
11. 11.Three temple bells ring every 24, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
12. 12.Three temple bells ring every 6, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
13. 13.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 15, 12 or 8.
14. 14.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 9, 15 or 12.
15. 15.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 8 or 10.
16. 16.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
17. 17.Sneha takes 50 seconds and Zoya takes 80 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?
18. 18.Three temple bells ring every 10, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
19. 19.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?
20. 20.Pooja takes 36 seconds and Vivaan 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?
21. 21.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?
22. 22.A hall floor is 140 cm long and 80 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 10, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
24. 24.Two tanks hold 140 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
25. 25.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
26. 26.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?
27. 27.Two tanks hold 45 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
28. 28.Manav takes 30 seconds and Karan takes 40 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?
29. 29.Saanvi takes 40 seconds and Vivaan takes 72 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?
30. 30.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
31. 31.Tara takes 45 seconds and Diya 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?
32. 32.Dev takes 45 seconds and Aarav 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?
33. 33.Vivaan takes 72 seconds and Rahul 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?
34. 34.Two tanks hold 80 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
35. 35.Tara takes 80 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?
36. 36.Three temple bells ring every 4, 18 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
37. 37.Three temple bells ring every 24, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
38. 38.Two tanks hold 360 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
39. 39.Kabir takes 30 seconds and Saanvi takes 80 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?
40. 40.Isha takes 40 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?

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