HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 124 · 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 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
2. 2.Isha takes 72 seconds and Priya 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?
3. 3.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 5 or 4.
4. 4.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?
5. 5.Three temple bells ring every 5, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
6. 6.Two tanks hold 175 litres and 125 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 10 litres and 25 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, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.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?
10. 10.Two tanks hold 80 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.Three temple bells ring every 8, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
12. 12.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?
13. 13.Two tanks hold 225 litres and 360 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 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
15. 15.Three temple bells ring every 6, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
16. 16.A hall floor is 420 cm long and 360 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
17. 17.Dev takes 72 seconds and Aarav 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.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 6 or 15.
19. 19.Two tanks hold 200 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
20. 20.Dev takes 54 seconds and Aarav 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?
21. 21.Three temple bells ring every 5, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
22. 22.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 8, 9 or 6.
23. 23.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 5.
24. 24.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 5 or 3.
25. 25.Three temple bells ring every 20, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
26. 26.Three temple bells ring every 24, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
27. 27.Three temple bells ring every 15, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
28. 28.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?
29. 29.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?
30. 30.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 3 or 5.
31. 31.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 10 or 9.
32. 32.Dev 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?
33. 33.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 6.
34. 34.Two tanks hold 405 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
35. 35.Two tanks hold 50 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
36. 36.Farhan takes 45 seconds and Vivaan 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?
37. 37.Two tanks hold 40 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
38. 38.Three temple bells ring every 5, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 10 or 9.
40. 40.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 6.

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