HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 355 · 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.Manav takes 50 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?
2. 2.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 9 or 3.
3. 3.Three temple bells ring every 5, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
4. 4.Diya takes 30 seconds and Rohan 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?
5. 5.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 8, 9 or 12.
6. 6.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
7. 7.Three temple bells ring every 15, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
8. 8.Three temple bells ring every 12, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.Three temple bells ring every 18, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
10. 10.Three temple bells ring every 8, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
11. 11.Aditya takes 48 seconds and Aarav 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?
12. 12.Three temple bells ring every 30, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
13. 13.Three temple bells ring every 6, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
14. 14.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 5.
15. 15.Priya takes 30 seconds and Kabir 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?
16. 16.Three temple bells ring every 24, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
17. 17.Three temple bells ring every 10, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
18. 18.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?
19. 19.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 9.
20. 20.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 6, 5 or 10.
21. 21.Meera takes 40 seconds and Rohan 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?
22. 22.Two tanks hold 180 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
23. 23.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 8 or 9.
24. 24.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 12 or 4.
25. 25.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 5 or 9.
26. 26.Three temple bells ring every 8, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
27. 27.Two tanks hold 80 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
28. 28.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 3 or 8.
29. 29.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 9, 10 or 3.
30. 30.A hall floor is 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
31. 31.A hall floor is 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
32. 32.Three temple bells ring every 24, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
33. 33.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 10, 4 or 12.
34. 34.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?
35. 35.Two tanks hold 200 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
36. 36.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 6.
37. 37.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 3.
38. 38.Three temple bells ring every 6, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.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?
40. 40.Kabir takes 40 seconds and Diya 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?

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