HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 39 · 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 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
2. 2.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 9 or 12.
3. 3.Two tanks hold 50 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
4. 4.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?
5. 5.Three temple bells ring every 18, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
6. 6.Three temple bells ring every 30, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
7. 7.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
8. 8.Three temple bells ring every 30, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
10. 10.Three temple bells ring every 9, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
11. 11.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 8 or 15.
12. 12.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
13. 13.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?
14. 14.A hall floor is 280 cm long and 200 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 3 when divided by 10, 8 or 15.
16. 16.Three temple bells ring every 24, 5 and 20 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 5, 10 or 3.
18. 18.Three temple bells ring every 8, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
19. 19.Two tanks hold 250 litres and 100 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 8 that leaves a remainder of 1 when divided by 8, 4 or 3.
21. 21.Sneha takes 30 seconds and Rohan takes 75 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?
22. 22.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
23. 23.Aditya takes 45 seconds and Kabir 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?
24. 24.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 12 or 9.
25. 25.Three temple bells ring every 10, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
26. 26.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?
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.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 9 or 10.
29. 29.Farhan takes 80 seconds and Priya 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?
30. 30.Three temple bells ring every 8, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
31. 31.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 10 or 15.
32. 32.Three temple bells ring every 4, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
33. 33.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 8.
34. 34.Three temple bells ring every 15, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.Two tanks hold 200 litres and 175 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 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
37. 37.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
38. 38.Ishaan takes 72 seconds and Kavya 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?
39. 39.Three temple bells ring every 4, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
40. 40.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

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