HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 250 · 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 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
2. 2.Two tanks hold 30 litres and 25 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 3 when divided by 12, 10 or 4.
4. 4.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 6.
5. 5.Three temple bells ring every 24, 5 and 12 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 9 that leaves a remainder of 1 when divided by 4, 9 or 6.
7. 7.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 12 or 9.
8. 8.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 10 or 15.
9. 9.Two tanks hold 70 litres and 50 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 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?
11. 11.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 15 or 3.
12. 12.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 5.
13. 13.Vivaan takes 45 seconds and Zoya 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?
14. 14.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?
15. 15.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 6 or 10.
16. 16.Two tanks hold 70 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
17. 17.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 5.
18. 18.Two tanks hold 125 litres and 200 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 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
20. 20.Three temple bells ring every 6, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
21. 21.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?
22. 22.Two tanks hold 120 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
23. 23.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
24. 24.Two tanks hold 45 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
25. 25.Two tanks hold 180 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
26. 26.Two tanks hold 90 litres and 405 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 210 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
28. 28.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
29. 29.Three temple bells ring every 10, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
30. 30.Three temple bells ring every 15, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
31. 31.Meera takes 50 seconds and Zoya 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?
32. 32.Ananya takes 60 seconds and Aarav 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?
33. 33.A hall floor is 225 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
34. 34.Find the smallest number bigger than 12 that leaves a remainder of 8 when divided by 10, 12 or 9.
35. 35.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 5.
36. 36.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 3 or 10.
37. 37.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 4.
38. 38.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 15, 8 or 12.
39. 39.Three temple bells ring every 8, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
40. 40.Two tanks hold 180 litres and 80 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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