HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 353 · 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.Three temple bells ring every 8, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
2. 2.Two tanks hold 135 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
3. 3.Three temple bells ring every 6, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
4. 4.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 15 or 3.
5. 5.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 4.
6. 6.Two tanks hold 320 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
7. 7.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 9 or 3.
8. 8.Three temple bells ring every 30, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.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?
10. 10.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 5.
11. 11.Two tanks hold 210 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
12. 12.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 5 or 4.
13. 13.Three temple bells ring every 5, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
14. 14.Aarav takes 36 seconds and Arjun 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.Two tanks hold 50 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
16. 16.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 12, 8 or 15.
17. 17.Three temple bells ring every 5, 6 and 9 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 10 that leaves a remainder of 2 when divided by 4, 10 or 9.
19. 19.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?
20. 20.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 9 or 12.
21. 21.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 9 or 3.
22. 22.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 4.
23. 23.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
24. 24.Three temple bells ring every 15, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
25. 25.Find the smallest number bigger than 15 that leaves a remainder of 8 when divided by 15, 9 or 12.
26. 26.Three temple bells ring every 6, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
27. 27.Three temple bells ring every 8, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
28. 28.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 4.
29. 29.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 5 or 3.
30. 30.Rahul takes 72 seconds and Karan 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?
31. 31.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?
32. 32.Manav takes 50 seconds and Rahul 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?
33. 33.Three temple bells ring every 6, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
34. 34.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
35. 35.Nisha takes 40 seconds and Dev takes 60 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?
36. 36.Three temple bells ring every 15, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
37. 37.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 5 or 15.
38. 38.Three temple bells ring every 4, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.A hall floor is 200 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
40. 40.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 10.

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