HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 301 · 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.Kabir takes 90 seconds and Arjun takes 36 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?
2. 2.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
3. 3.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 8 or 9.
4. 4.Two tanks hold 90 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
5. 5.Three temple bells ring every 30, 20 and 6 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 15 that leaves a remainder of 2 when divided by 6, 15 or 3.
7. 7.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
8. 8.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 3.
9. 9.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 6 or 8.
10. 10.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 6 or 9.
11. 11.Three temple bells ring every 15, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
12. 12.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 10, 15 or 5.
13. 13.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
14. 14.Two tanks hold 210 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
15. 15.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
16. 16.A hall floor is 200 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
17. 17.Three temple bells ring every 6, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
18. 18.Sneha takes 48 seconds and Meera 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?
19. 19.Rohan takes 30 seconds and Saanvi takes 36 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?
20. 20.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
21. 21.Two tanks hold 15 litres and 10 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 160 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
23. 23.Two tanks hold 250 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
24. 24.Meera takes 40 seconds and Zoya takes 75 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.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 4 or 5.
26. 26.Three temple bells ring every 8, 5 and 24 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 15 that leaves a remainder of 1 when divided by 6, 5 or 15.
28. 28.Two tanks hold 105 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
29. 29.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
30. 30.Two tanks hold 40 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
31. 31.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 6 or 9.
32. 32.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 3 or 6.
33. 33.Tara takes 80 seconds and Karan 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?
34. 34.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?
35. 35.Three temple bells ring every 12, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
36. 36.A hall floor is 400 cm long and 150 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, 24 and 30 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 10 that leaves a remainder of 1 when divided by 4, 10 or 8.
39. 39.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
40. 40.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

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