HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 234 · 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 350 cm long and 250 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 4 when divided by 15, 9 or 10.
3. 3.A hall floor is 320 cm long and 280 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 9 that leaves a remainder of 1 when divided by 9, 6 or 8.
5. 5.Aditya takes 36 seconds and Saanvi 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?
6. 6.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?
7. 7.Two tanks hold 320 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
8. 8.Ishaan takes 75 seconds and Kavya 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?
9. 9.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 3 or 6.
10. 10.Three temple bells ring every 18, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
11. 11.Three temple bells ring every 12, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
12. 12.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
13. 13.Pooja takes 80 seconds and Diya takes 48 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?
14. 14.Three temple bells ring every 10, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
15. 15.Two tanks hold 120 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
16. 16.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 6.
17. 17.A hall floor is 360 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
18. 18.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?
19. 19.Two tanks hold 75 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
20. 20.A hall floor is 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
21. 21.Two tanks hold 90 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
22. 22.Three temple bells ring every 30, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 9.
24. 24.Three temple bells ring every 5, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
25. 25.Three temple bells ring every 20, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
26. 26.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?
27. 27.Three temple bells ring every 24, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
28. 28.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 8 or 6.
29. 29.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 6 or 9.
30. 30.Zoya takes 60 seconds and Ananya 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?
31. 31.Three temple bells ring every 18, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
32. 32.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 5 or 15.
33. 33.Three temple bells ring every 30, 24 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 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
35. 35.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
36. 36.Three temple bells ring every 4, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
37. 37.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
38. 38.Tara takes 72 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?
39. 39.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 5.
40. 40.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?

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