HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 407 · 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 350 cm long and 250 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 10, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
3. 3.A hall floor is 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
4. 4.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?
5. 5.Three temple bells ring every 8, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
6. 6.Two tanks hold 70 litres and 90 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 70 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
8. 8.Three temple bells ring every 4, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.Three temple bells ring every 9, 18 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
10. 10.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 3.
11. 11.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
12. 12.Two tanks hold 60 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
13. 13.Aditya takes 45 seconds and Diya 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?
14. 14.A hall floor is 175 cm long and 100 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 2 when divided by 10, 5 or 12.
16. 16.Three temple bells ring every 30, 8 and 5 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 10 that leaves a remainder of 1 when divided by 10, 4 or 6.
18. 18.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 4 or 9.
19. 19.Two tanks hold 150 litres and 120 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 70 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
21. 21.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
22. 22.Three temple bells ring every 8, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.Two tanks hold 60 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
24. 24.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
25. 25.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?
26. 26.Three temple bells ring every 20, 8 and 5 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 10 that leaves a remainder of 4 when divided by 6, 10 or 5.
28. 28.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 8 or 6.
29. 29.Two tanks hold 180 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
30. 30.Three temple bells ring every 30, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
31. 31.Two tanks hold 350 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 15 that leaves a remainder of 1 when divided by 15, 3 or 12.
33. 33.Isha takes 48 seconds and Pooja 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?
34. 34.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
35. 35.Two tanks hold 140 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
36. 36.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
37. 37.Aarav takes 30 seconds and Diya 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?
38. 38.Three temple bells ring every 4, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.Three temple bells ring every 20, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
40. 40.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?

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