HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 88 · 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 10 that leaves a remainder of 2 when divided by 9, 5 or 10.
2. 2.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 6, 9 or 15.
3. 3.Three temple bells ring every 20, 6 and 4 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 3, 4 or 12.
5. 5.Two tanks hold 180 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
6. 6.Karan takes 80 seconds and Vivaan 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?
7. 7.A hall floor is 280 cm long and 80 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 4, 15 or 9.
9. 9.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 9 or 10.
10. 10.Three temple bells ring every 6, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
11. 11.Two tanks hold 80 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
12. 12.Three temple bells ring every 5, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
13. 13.Two tanks hold 35 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
14. 14.Two tanks hold 350 litres and 100 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 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
16. 16.Priya takes 40 seconds and Manav 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?
17. 17.Three temple bells ring every 24, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
18. 18.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
19. 19.Two tanks hold 10 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
20. 20.Aarav takes 36 seconds and Zoya 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?
21. 21.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?
22. 22.Three temple bells ring every 15, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.Three temple bells ring every 24, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
24. 24.Dev takes 45 seconds and Ananya 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?
25. 25.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?
26. 26.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 9 or 10.
27. 27.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
28. 28.Three temple bells ring every 9, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
29. 29.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?
30. 30.Two tanks hold 15 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
31. 31.Two tanks hold 120 litres and 320 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 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
33. 33.Two tanks hold 180 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
34. 34.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 5 or 3.
35. 35.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 6 or 4.
36. 36.Two tanks hold 20 litres and 45 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 5, 8 or 12.
38. 38.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
39. 39.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 5.
40. 40.Tara takes 72 seconds and Pooja 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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