HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 184 · 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 15 that leaves a remainder of 2 when divided by 3, 6 or 15.
2. 2.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 6.
3. 3.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
4. 4.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
5. 5.Three temple bells ring every 4, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
6. 6.Two tanks hold 75 litres and 105 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 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
8. 8.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?
9. 9.Two tanks hold 200 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
10. 10.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 4 or 8.
11. 11.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 8 or 4.
12. 12.Three temple bells ring every 4, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
13. 13.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?
14. 14.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
15. 15.Two tanks hold 75 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.Diya takes 90 seconds and Pooja takes 80 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 40 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
18. 18.Two tanks hold 160 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
19. 19.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?
20. 20.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 4.
21. 21.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 12 or 8.
22. 22.Three temple bells ring every 10, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
24. 24.Pooja takes 40 seconds and Diya takes 45 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 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
26. 26.Three temple bells ring every 5, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
27. 27.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 3.
28. 28.Three temple bells ring every 15, 5 and 12 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 10 that leaves a remainder of 2 when divided by 6, 3 or 10.
30. 30.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 3 or 15.
31. 31.Kabir takes 30 seconds and Farhan 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?
32. 32.Two tanks hold 140 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
33. 33.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?
34. 34.Three temple bells ring every 9, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.Two tanks hold 30 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
36. 36.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?
37. 37.Three temple bells ring every 30, 5 and 12 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 12 that leaves a remainder of 2 when divided by 8, 12 or 10.
39. 39.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 9, 5 or 10.
40. 40.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?

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