HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 253 · 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.Two tanks hold 40 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
2. 2.Priya takes 60 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?
3. 3.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 9, 4 or 10.
4. 4.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 9 or 4.
5. 5.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 6, 9 or 10.
6. 6.Two tanks hold 20 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
7. 7.Diya takes 90 seconds and Rohan 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?
8. 8.Two tanks hold 75 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
9. 9.Dev takes 50 seconds and Rahul 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?
10. 10.Three temple bells ring every 30, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
11. 11.Two tanks hold 210 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
12. 12.Three temple bells ring every 4, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
13. 13.A hall floor is 125 cm long and 50 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 15 that leaves a remainder of 1 when divided by 6, 4 or 15.
15. 15.Nisha takes 72 seconds and Pooja 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?
16. 16.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
17. 17.Three temple bells ring every 15, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
18. 18.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 6, 8 or 5.
19. 19.Two tanks hold 100 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
20. 20.Three temple bells ring every 24, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
21. 21.Three temple bells ring every 12, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
22. 22.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
23. 23.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 5 or 9.
24. 24.Aarav takes 72 seconds and Vivaan 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?
25. 25.Three temple bells ring every 8, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
26. 26.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 4 or 5.
27. 27.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 8 or 5.
28. 28.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 15 or 3.
29. 29.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 10 or 8.
30. 30.A hall floor is 150 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 15 that leaves a remainder of 4 when divided by 15, 5 or 8.
32. 32.Diya takes 54 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?
33. 33.Three temple bells ring every 4, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
34. 34.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?
35. 35.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 5 or 8.
36. 36.Three temple bells ring every 9, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
37. 37.Two tanks hold 200 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
38. 38.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 10 or 15.
39. 39.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 3 or 6.
40. 40.Rahul takes 54 seconds and Farhan 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?

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