HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 399 · 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.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?
2. 2.Two tanks hold 360 litres and 80 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 4, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
4. 4.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?
5. 5.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 5.
6. 6.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 3.
7. 7.Two tanks hold 270 litres and 210 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 15, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.Two tanks hold 40 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
10. 10.Two tanks hold 270 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
11. 11.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 5, 6 or 3.
12. 12.Three temple bells ring every 5, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
13. 13.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 6 or 5.
14. 14.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 3.
15. 15.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 3 or 5.
16. 16.Three temple bells ring every 12, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
17. 17.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 3.
18. 18.Two tanks hold 90 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
19. 19.Two tanks hold 250 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
20. 20.Two tanks hold 25 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
21. 21.A hall floor is 200 cm long and 150 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 5, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 5 or 12.
24. 24.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 5 or 12.
25. 25.Three temple bells ring every 10, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
26. 26.Two tanks hold 30 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
27. 27.Two tanks hold 80 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
28. 28.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 8, 6 or 15.
29. 29.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 8 or 5.
30. 30.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 8 or 6.
31. 31.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 3 or 15.
32. 32.Priya takes 48 seconds and Karan 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?
33. 33.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
34. 34.Three temple bells ring every 4, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.Three temple bells ring every 10, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
36. 36.A hall floor is 150 cm long and 60 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 6, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
38. 38.Two tanks hold 105 litres and 135 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 15 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
40. 40.Two tanks hold 360 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

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