HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 210 · 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 180 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
2. 2.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
3. 3.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
4. 4.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?
5. 5.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 10 or 12.
6. 6.Two tanks hold 360 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
7. 7.Zoya takes 45 seconds and Ananya takes 36 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.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 8 or 3.
9. 9.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
10. 10.Two tanks hold 405 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
11. 11.Two tanks hold 10 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
12. 12.Two tanks hold 250 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
13. 13.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
14. 14.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 12, 6 or 9.
15. 15.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 5 or 8.
16. 16.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 5, 4 or 9.
17. 17.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 5.
18. 18.Three temple bells ring every 12, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
19. 19.Two tanks hold 60 litres and 150 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 15 that leaves a remainder of 2 when divided by 4, 6 or 15.
21. 21.Three temple bells ring every 8, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
22. 22.Three temple bells ring every 10, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.Two tanks hold 120 litres and 320 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 8, 20 and 4 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 10 that leaves a remainder of 1 when divided by 10, 3 or 5.
26. 26.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?
27. 27.Two tanks hold 160 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
28. 28.Two tanks hold 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
29. 29.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
30. 30.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?
31. 31.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 6 or 10.
32. 32.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 15 or 3.
34. 34.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 4.
35. 35.Three temple bells ring every 24, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
36. 36.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 8 or 3.
37. 37.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?
38. 38.Aditya 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?
39. 39.Tara takes 36 seconds and Pooja 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?
40. 40.Two tanks hold 120 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

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