HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 536 · 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 2 when divided by 15, 8 or 10.
2. 2.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
3. 3.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?
4. 4.Isha takes 90 seconds and Priya 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?
5. 5.Two tanks hold 225 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
6. 6.Three temple bells ring every 4, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
7. 7.Three temple bells ring every 18, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
8. 8.Three temple bells ring every 30, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
9. 9.Three temple bells ring every 4, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
10. 10.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 10 or 12.
11. 11.Two tanks hold 225 litres and 135 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 15 that leaves a remainder of 2 when divided by 15, 12 or 5.
13. 13.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 4.
14. 14.Two tanks hold 90 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
15. 15.Three temple bells ring every 15, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
16. 16.Two tanks hold 75 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
17. 17.Two tanks hold 150 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
18. 18.Vivaan takes 45 seconds and Karan 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?
19. 19.Two tanks hold 80 litres and 200 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 45 litres and 40 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 12 that leaves a remainder of 3 when divided by 10, 5 or 12.
22. 22.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?
23. 23.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 3 or 10.
24. 24.Three temple bells ring every 8, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
25. 25.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?
26. 26.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 8 or 3.
27. 27.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?
28. 28.Meera takes 75 seconds and Saanvi takes 45 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?
29. 29.Three temple bells ring every 18, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
30. 30.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?
31. 31.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 5 or 10.
32. 32.Three temple bells ring every 12, 20 and 8 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 3 when divided by 4, 10 or 12.
34. 34.Three temple bells ring every 30, 6 and 20 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 5 that leaves a remainder of 1 when divided by 5, 3 or 4.
36. 36.Isha takes 75 seconds and Priya 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?
37. 37.A hall floor is 175 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
38. 38.Three temple bells ring every 30, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.Three temple bells ring every 18, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
40. 40.Two tanks hold 150 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

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