HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 467 · 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 280 cm long and 120 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 2 when divided by 5, 10 or 15.
3. 3.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 8, 9 or 3.
4. 4.Find the smallest number bigger than 12 that leaves a remainder of 6 when divided by 9, 12 or 8.
5. 5.Vivaan 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?
6. 6.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 10 or 15.
7. 7.Two tanks hold 60 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
8. 8.Two tanks hold 25 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
9. 9.Two tanks hold 60 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
10. 10.Two tanks hold 20 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
11. 11.Vivaan takes 90 seconds and Rahul takes 80 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?
12. 12.Aarav takes 54 seconds and Saanvi takes 72 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?
13. 13.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 4 or 15.
14. 14.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 3 or 12.
15. 15.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?
16. 16.Rahul takes 36 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?
17. 17.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
18. 18.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
19. 19.Two tanks hold 10 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
20. 20.Two tanks hold 10 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
21. 21.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?
22. 22.Three temple bells ring every 10, 24 and 30 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 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
24. 24.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
25. 25.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 5, 8 or 4.
26. 26.Three temple bells ring every 15, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
27. 27.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 8 or 15.
28. 28.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 4.
29. 29.Two tanks hold 400 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
30. 30.Three temple bells ring every 4, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
31. 31.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 6, 8 or 15.
32. 32.Three temple bells ring every 4, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
33. 33.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 4 or 10.
34. 34.Three temple bells ring every 6, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.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?
36. 36.Two tanks hold 15 litres and 25 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 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
38. 38.Three temple bells ring every 8, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.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?
40. 40.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?

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