HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 101 · 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 350 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
2. 2.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 10, 5 or 12.
3. 3.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 3 or 5.
4. 4.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 15 or 4.
5. 5.Three temple bells ring every 20, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
6. 6.Two tanks hold 125 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
7. 7.Two tanks hold 240 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.Three temple bells ring every 4, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.Three temple bells ring every 10, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
10. 10.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?
11. 11.Zoya takes 45 seconds and Kavya takes 50 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.Three temple bells ring every 5, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
13. 13.Two tanks hold 315 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
14. 14.Meera takes 48 seconds and Aarav 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?
15. 15.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 4 or 15.
16. 16.Karan takes 48 seconds and Rahul 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.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
18. 18.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?
19. 19.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 10 or 4.
20. 20.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 6, 4 or 12.
21. 21.Three temple bells ring every 9, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
22. 22.Kabir takes 48 seconds and Pooja 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?
23. 23.Rahul takes 45 seconds and Kavya 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?
24. 24.Two tanks hold 50 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
25. 25.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 4 or 5.
26. 26.Three temple bells ring every 30, 15 and 20 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 4 when divided by 10, 15 or 9.
28. 28.Ananya takes 40 seconds and Rohan 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?
29. 29.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 3 or 15.
30. 30.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?
31. 31.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 10, 12 or 3.
32. 32.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?
33. 33.Three temple bells ring every 6, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
34. 34.Two tanks hold 125 litres and 75 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 15 that leaves a remainder of 3 when divided by 15, 12 or 10.
36. 36.Three temple bells ring every 6, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
37. 37.Three temple bells ring every 9, 30 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
38. 38.Farhan takes 72 seconds and Priya 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?
39. 39.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 8, 9 or 3.
40. 40.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 9, 10 or 15.

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