HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 89 · 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 3 when divided by 6, 5 or 15.
2. 2.Tara takes 72 seconds and Dev takes 30 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?
3. 3.Two tanks hold 200 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
4. 4.Kabir takes 72 seconds and Ananya takes 90 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?
5. 5.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 12.
6. 6.Two tanks hold 240 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
7. 7.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 10.
8. 8.Vivaan takes 72 seconds and Sneha takes 90 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?
9. 9.Zoya takes 72 seconds and Karan 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?
10. 10.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 5 or 15.
11. 11.Two tanks hold 50 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
12. 12.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?
13. 13.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 8, 10 or 6.
14. 14.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
15. 15.Two tanks hold 90 litres and 20 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 5, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
17. 17.Karan takes 36 seconds and Diya 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?
18. 18.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 8.
19. 19.Three temple bells ring every 12, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
20. 20.Two tanks hold 140 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
21. 21.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 4 or 5.
22. 22.Two tanks hold 200 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
23. 23.Three temple bells ring every 20, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
24. 24.Three temple bells ring every 10, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
25. 25.A hall floor is 100 cm long and 75 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 5 that leaves a remainder of 1 when divided by 3, 5 or 4.
27. 27.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 4 or 12.
28. 28.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
29. 29.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 9.
30. 30.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
31. 31.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 8 or 12.
32. 32.A hall floor is 210 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
33. 33.Three temple bells ring every 8, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
34. 34.Three temple bells ring every 24, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.Two tanks hold 60 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
36. 36.Two tanks hold 150 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
37. 37.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 3 or 12.
38. 38.Three temple bells ring every 24, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.Sneha takes 30 seconds and Rahul 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?
40. 40.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 8 or 5.

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