HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 103 · 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 300 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
2. 2.Two tanks hold 250 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
3. 3.Two tanks hold 40 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
4. 4.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?
5. 5.Three temple bells ring every 12, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
6. 6.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
7. 7.Find the smallest number bigger than 15 that leaves a remainder of 8 when divided by 10, 15 or 9.
8. 8.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
9. 9.Two tanks hold 200 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
10. 10.Two tanks hold 25 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
11. 11.Aditya takes 45 seconds and Saanvi 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?
12. 12.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 8.
13. 13.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
14. 14.Three temple bells ring every 10, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
15. 15.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 10.
16. 16.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?
17. 17.Two tanks hold 180 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
18. 18.Three temple bells ring every 5, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
19. 19.Two tanks hold 35 litres and 10 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, 3 or 5.
21. 21.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 8.
22. 22.Three temple bells ring every 10, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.Three temple bells ring every 4, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
24. 24.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
25. 25.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 5, 3 or 6.
26. 26.Zoya takes 60 seconds and Ishaan 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?
27. 27.Three temple bells ring every 10, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
28. 28.Karan takes 48 seconds and Saanvi 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?
29. 29.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 10, 6 or 15.
30. 30.Two tanks hold 90 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
31. 31.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 12, 8 or 9.
32. 32.Two tanks hold 15 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
33. 33.A hall floor is 200 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
34. 34.Three temple bells ring every 9, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.Two tanks hold 280 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
36. 36.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 8, 12 or 9.
37. 37.Three temple bells ring every 8, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
38. 38.Three temple bells ring every 18, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.Three temple bells ring every 8, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
40. 40.Manav takes 45 seconds and Kavya 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?

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