HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 430 · 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 8 that leaves a remainder of 3 when divided by 8, 5 or 6.
2. 2.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
3. 3.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
4. 4.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 10 or 12.
5. 5.Three temple bells ring every 6, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
6. 6.Three temple bells ring every 30, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
7. 7.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 8 or 12.
8. 8.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 6 or 4.
9. 9.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?
10. 10.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 4 or 15.
11. 11.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 6 or 12.
12. 12.Two tanks hold 20 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
13. 13.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 9 or 10.
14. 14.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
15. 15.Two tanks hold 140 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
16. 16.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?
17. 17.Three temple bells ring every 20, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
18. 18.Two tanks hold 100 litres and 350 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 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
20. 20.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
21. 21.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 5 or 10.
22. 22.Three temple bells ring every 24, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.Saanvi takes 72 seconds and Aditya takes 54 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 75 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
25. 25.Three temple bells ring every 10, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
26. 26.Ishaan takes 75 seconds and Sneha 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?
27. 27.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 6.
28. 28.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 8 or 6.
29. 29.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?
30. 30.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?
31. 31.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?
32. 32.Three temple bells ring every 10, 15 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
33. 33.Two tanks hold 315 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
34. 34.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 8, 15 or 12.
35. 35.Three temple bells ring every 8, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
36. 36.Saanvi takes 54 seconds and Rahul 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?
37. 37.Three temple bells ring every 6, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
38. 38.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 12.
39. 39.A hall floor is 420 cm long and 180 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 8 that leaves a remainder of 2 when divided by 3, 8 or 6.

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