HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 552 · 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 100 cm long and 60 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 15 that leaves a remainder of 1 when divided by 3, 15 or 12.
3. 3.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?
4. 4.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 9, 12 or 15.
5. 5.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 8 or 12.
6. 6.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
7. 7.Two tanks hold 180 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
8. 8.A hall floor is 210 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
9. 9.Two tanks hold 20 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
10. 10.Vivaan takes 54 seconds and Farhan 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?
11. 11.Three temple bells ring every 20, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
12. 12.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 10, 12 or 6.
13. 13.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?
14. 14.Two tanks hold 30 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
15. 15.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 12 or 8.
16. 16.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?
17. 17.Find the smallest number bigger than 6 that leaves a remainder of 3 when divided by 6, 4 or 5.
18. 18.Diya takes 72 seconds and Rohan 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?
19. 19.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?
20. 20.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 12 or 3.
21. 21.Tara takes 45 seconds and Farhan 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?
22. 22.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?
23. 23.Two tanks hold 35 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
24. 24.Three temple bells ring every 15, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
25. 25.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 8, 3 or 9.
26. 26.Dev takes 40 seconds and Aditya 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?
27. 27.Two tanks hold 350 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
28. 28.Three temple bells ring every 9, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
29. 29.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
30. 30.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
31. 31.Two tanks hold 450 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
32. 32.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 6.
33. 33.Vivaan takes 45 seconds and Pooja 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?
34. 34.Two tanks hold 45 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
35. 35.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?
36. 36.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
37. 37.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
38. 38.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 3 or 4.
39. 39.Two tanks hold 100 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
40. 40.Three temple bells ring every 24, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

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