HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 137 · 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.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 10 or 3.
2. 2.Two tanks hold 100 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
3. 3.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 9.
4. 4.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 6 or 3.
5. 5.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
6. 6.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
7. 7.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
8. 8.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 15 or 6.
9. 9.Three temple bells ring every 5, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
10. 10.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 6.
11. 11.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?
12. 12.Two tanks hold 175 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
13. 13.Three temple bells ring every 18, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
14. 14.A hall floor is 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
15. 15.Arjun takes 48 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?
16. 16.Arjun takes 50 seconds and Ananya 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?
17. 17.Two tanks hold 15 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
18. 18.Three temple bells ring every 10, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
19. 19.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 3.
20. 20.Three temple bells ring every 30, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
21. 21.A hall floor is 350 cm long and 200 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 30, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
24. 24.Arjun takes 72 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?
25. 25.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
26. 26.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 8 or 3.
27. 27.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?
28. 28.Three temple bells ring every 9, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
29. 29.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 4.
30. 30.Two tanks hold 45 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
31. 31.Three temple bells ring every 5, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
32. 32.Three temple bells ring every 8, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
33. 33.Two tanks hold 280 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
34. 34.Three temple bells ring every 30, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.Three temple bells ring every 20, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
36. 36.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?
37. 37.Three temple bells ring every 20, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
38. 38.Two tanks hold 20 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
39. 39.Two tanks hold 120 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
40. 40.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 12 or 5.

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