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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 436 · 40 questions
TalentJR

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).

NameDateTime takenScore ___ / 40
  1. 1.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 4 or 8.
  2. 2.Three temple bells ring every 10, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 12 or 6.
  4. 4.A hall floor is 180 cm long and 120 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 10 that leaves a remainder of 1 when divided by 3, 4 or 10.
  6. 6.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Saanvi takes 72 seconds and Farhan 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?
  8. 8.Three temple bells ring every 20, 12 and 15 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, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Arjun takes 54 seconds and Kavya 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?
  11. 11.Zoya takes 80 seconds and Tara 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?
  12. 12.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 5, 9 or 4.
  13. 13.Nisha takes 75 seconds and Saanvi 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?
  14. 14.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?
  15. 15.Three temple bells ring every 9, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 18, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.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?
  18. 18.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?
  19. 19.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?
  20. 20.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 5 or 12.
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 15 or 4.
  22. 22.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Isha takes 30 seconds and Karan 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.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?
  25. 25.Two tanks hold 90 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.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?
  27. 27.Two tanks hold 350 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 8, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 35 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Nisha takes 50 seconds and Sneha 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?
  31. 31.Three temple bells ring every 15, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 240 litres and 200 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 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Diya takes 36 seconds and Arjun 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?
  35. 35.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 4 or 5.
  36. 36.Two tanks hold 225 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Diya takes 40 seconds and Arjun 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?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 15 or 10.
  39. 39.Karan takes 40 seconds and Sneha takes 60 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?
  40. 40.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 9.

Answer key

  1. 123
  2. 120
  3. 14
  4. 6
  5. 61
  6. 56
  7. 360
  8. 60
  9. 24
  10. 216
  11. 240
  12. 182
  13. 600
  14. 20
  15. 72
  16. 36
  17. 90
  18. 30
  19. 20
  20. 61
  21. 62
  22. 56
  23. 360
  24. 10
  25. 10
  26. 56
  27. 50
  28. 120
  29. 5
  30. 150
  31. 120
  32. 40
  33. 20
  34. 180
  35. 21
  36. 25
  37. 360
  38. 63
  39. 120
  40. 92

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