HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 74 · 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.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 9, 10 or 4.
2. 2.A hall floor is 270 cm long and 225 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 2 when divided by 12, 10 or 3.
4. 4.Three temple bells ring every 4, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
5. 5.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 8 or 3.
6. 6.Saanvi takes 54 seconds and Nisha 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?
7. 7.Zoya takes 40 seconds and Arjun 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?
8. 8.Three temple bells ring every 8, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.A hall floor is 200 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 75 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.Two tanks hold 240 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
12. 12.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
13. 13.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 12 or 15.
14. 14.Two tanks hold 120 litres and 45 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 6, 5 or 12.
16. 16.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 6.
17. 17.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
18. 18.Three temple bells ring every 10, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
19. 19.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
20. 20.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?
21. 21.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
22. 22.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?
23. 23.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 3 or 12.
24. 24.Two tanks hold 300 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
25. 25.Aarav takes 80 seconds and Kavya 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?
26. 26.A hall floor is 400 cm long and 150 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 6, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
28. 28.Three temple bells ring every 12, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
29. 29.Three temple bells ring every 15, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
30. 30.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 8.
31. 31.Three temple bells ring every 15, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
32. 32.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?
33. 33.Two tanks hold 180 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
34. 34.Zoya takes 50 seconds and Priya 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?
35. 35.Find the smallest number bigger than 15 that leaves a remainder of 8 when divided by 15, 9 or 10.
36. 36.Two tanks hold 75 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
37. 37.Two tanks hold 210 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
38. 38.Two tanks hold 135 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
39. 39.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
40. 40.Two tanks hold 50 litres and 125 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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