HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 116 · 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.Two tanks hold 160 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
2. 2.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?
3. 3.Three temple bells ring every 10, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
4. 4.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?
5. 5.Two tanks hold 30 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
6. 6.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 8.
7. 7.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 4.
8. 8.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 3, 4 or 5.
9. 9.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 5 or 12.
10. 10.Two tanks hold 105 litres and 60 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 48 seconds and Sneha 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?
12. 12.A hall floor is 480 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
13. 13.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 9 or 12.
14. 14.Three temple bells ring every 12, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
15. 15.Three temple bells ring every 30, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
16. 16.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?
17. 17.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
18. 18.Three temple bells ring every 4, 12 and 20 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 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
20. 20.Two tanks hold 80 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
21. 21.Three temple bells ring every 8, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
22. 22.Ishaan takes 45 seconds and Karan 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?
23. 23.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 10.
24. 24.Three temple bells ring every 5, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
25. 25.Three temple bells ring every 30, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
26. 26.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?
27. 27.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?
28. 28.Tara takes 72 seconds and Rohan 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?
29. 29.Three temple bells ring every 30, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
30. 30.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 5, 9 or 3.
31. 31.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
32. 32.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 12 or 6.
33. 33.Three temple bells ring every 5, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
34. 34.Three temple bells ring every 8, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.Karan takes 50 seconds and Sneha 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?
36. 36.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 4 or 9.
37. 37.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 3 or 15.
38. 38.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
39. 39.Aditya takes 75 seconds and Ishaan 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?
40. 40.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?

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