HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 27 · 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.Nisha takes 30 seconds and Zoya 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?
2. 2.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 6 or 4.
3. 3.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 8 or 10.
4. 4.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 12.
5. 5.Three temple bells ring every 24, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
6. 6.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 12 or 10.
7. 7.Two tanks hold 200 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
8. 8.Dev takes 36 seconds and Meera 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?
9. 9.Two tanks hold 50 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
10. 10.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
11. 11.A hall floor is 175 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
12. 12.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 6, 3 or 8.
13. 13.Arjun takes 72 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?
14. 14.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 4 or 10.
15. 15.Karan takes 80 seconds and Diya 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?
16. 16.Three temple bells ring every 5, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
17. 17.Rahul takes 54 seconds and Diya 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?
18. 18.Two tanks hold 135 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
19. 19.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
20. 20.Saanvi takes 80 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?
21. 21.Three temple bells ring every 5, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
22. 22.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 10.
23. 23.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 3 or 6.
24. 24.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 6, 8 or 10.
25. 25.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 3.
26. 26.Three temple bells ring every 12, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
27. 27.Three temple bells ring every 4, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
28. 28.Isha takes 72 seconds and Dev 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?
29. 29.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?
30. 30.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?
31. 31.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 12.
32. 32.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 5 or 9.
33. 33.Three temple bells ring every 15, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
34. 34.Two tanks hold 30 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
35. 35.Three temple bells ring every 6, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
36. 36.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?
37. 37.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 9, 12 or 6.
38. 38.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 15 or 10.
39. 39.Three temple bells ring every 10, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
40. 40.Three temple bells ring every 30, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

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