HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 486 · 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.Meera takes 75 seconds and Kabir 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?
2. 2.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 8 or 15.
3. 3.Three temple bells ring every 24, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
4. 4.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 3 or 12.
5. 5.Two tanks hold 315 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
6. 6.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?
7. 7.Saanvi takes 90 seconds and Dev 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?
8. 8.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
9. 9.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
10. 10.Three temple bells ring every 4, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
11. 11.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?
12. 12.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 5 or 8.
13. 13.Two tanks hold 270 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
14. 14.Three temple bells ring every 5, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
15. 15.Two tanks hold 75 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
16. 16.Ishaan takes 48 seconds and Tara 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?
17. 17.Two tanks hold 160 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
18. 18.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 3 or 4.
19. 19.Two tanks hold 25 litres and 45 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 360 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
21. 21.Two tanks hold 105 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
22. 22.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?
23. 23.Aditya takes 30 seconds and Dev 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?
24. 24.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 3.
25. 25.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?
26. 26.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 9 or 12.
27. 27.Three temple bells ring every 5, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
28. 28.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
29. 29.Two tanks hold 140 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
30. 30.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 10 or 5.
31. 31.Two tanks hold 50 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
32. 32.A hall floor is 420 cm long and 360 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
33. 33.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 5 or 4.
34. 34.Three temple bells ring every 18, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
35. 35.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 4 or 9.
36. 36.Saanvi takes 45 seconds and Kabir takes 50 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?
37. 37.Two tanks hold 120 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
38. 38.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 5 or 9.
39. 39.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 5, 10 or 6.
40. 40.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

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