HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 533 · 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.Three temple bells ring every 18, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
2. 2.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
3. 3.Three temple bells ring every 5, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
4. 4.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?
5. 5.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 5.
6. 6.Two tanks hold 450 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
7. 7.Three temple bells ring every 6, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
8. 8.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?
9. 9.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 5 or 4.
10. 10.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?
11. 11.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 8.
12. 12.Arjun takes 30 seconds and Meera 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?
13. 13.Two tanks hold 10 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
14. 14.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 3.
15. 15.Karan takes 45 seconds and Priya 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?
16. 16.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 5 or 9.
17. 17.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?
18. 18.Two tanks hold 405 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
19. 19.Two tanks hold 270 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
20. 20.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 5.
21. 21.Two tanks hold 210 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
22. 22.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 3 or 12.
23. 23.Saanvi takes 50 seconds and Nisha 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?
24. 24.Three temple bells ring every 24, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
25. 25.Three temple bells ring every 10, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
26. 26.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 9, 6 or 10.
27. 27.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 9 or 3.
28. 28.Three temple bells ring every 5, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
29. 29.Diya takes 30 seconds and Aarav 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?
30. 30.Two tanks hold 105 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 1 when divided by 3, 4 or 9.
32. 32.Two tanks hold 25 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
33. 33.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
34. 34.Ananya takes 80 seconds and Ishaan 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?
35. 35.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 4 or 10.
36. 36.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
37. 37.Two tanks hold 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
38. 38.Three temple bells ring every 30, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
39. 39.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
40. 40.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 5, 3 or 4.

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