HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 526 · 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 40 litres and 45 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 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
3. 3.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 8.
4. 4.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
5. 5.Two tanks hold 80 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
6. 6.Three temple bells ring every 12, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
7. 7.Farhan takes 36 seconds and Saanvi 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?
8. 8.Three temple bells ring every 24, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.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?
10. 10.Sneha takes 72 seconds and Saanvi 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?
11. 11.Three temple bells ring every 10, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
12. 12.Two tanks hold 60 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
13. 13.Three temple bells ring every 30, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
14. 14.Rohan takes 48 seconds and Zoya 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?
15. 15.Three temple bells ring every 8, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
16. 16.Three temple bells ring every 30, 20 and 4 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 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
18. 18.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 3 or 15.
19. 19.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 4.
20. 20.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 8 or 15.
21. 21.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 3.
22. 22.Zoya takes 80 seconds and Vivaan 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?
23. 23.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 8.
24. 24.Two tanks hold 90 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
25. 25.Two tanks hold 315 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
26. 26.Three temple bells ring every 9, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
27. 27.A hall floor is 120 cm long and 80 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 12 that leaves a remainder of 4 when divided by 9, 12 or 10.
29. 29.Two tanks hold 280 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
30. 30.Two tanks hold 210 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
31. 31.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
32. 32.Two tanks hold 40 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
33. 33.Three temple bells ring every 30, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
34. 34.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
35. 35.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 3.
36. 36.A hall floor is 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
37. 37.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?
38. 38.Three temple bells ring every 24, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.Pooja takes 75 seconds and Arjun 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?
40. 40.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 9.

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