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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 175 · 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.Three temple bells ring every 18, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 4, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 4, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 360 cm long and 225 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 15 that leaves a remainder of 2 when divided by 5, 3 or 15.
  6. 6.Rahul takes 72 seconds and Kabir 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?
  7. 7.Three temple bells ring every 30, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 4, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 30, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.A hall floor is 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Rohan takes 54 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?
  12. 12.Vivaan takes 90 seconds and Aarav takes 54 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.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Diya takes 75 seconds and Pooja 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?
  15. 15.Dev takes 45 seconds and Aarav 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?
  16. 16.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 5.
  18. 18.Two tanks hold 280 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Three temple bells ring every 12, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 15 or 4.
  21. 21.Two tanks hold 360 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.A hall floor is 300 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Two tanks hold 15 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 12, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.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?
  26. 26.Three temple bells ring every 12, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 20, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 4, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 24, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 12 or 4.
  31. 31.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 10 or 8.
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 9, 12 or 15.
  33. 33.Aditya takes 45 seconds and Saanvi 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?
  34. 34.Two tanks hold 100 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.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?
  36. 36.Two tanks hold 200 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 9 or 5.
  39. 39.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?
  40. 40.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 12 or 4.

Answer key

  1. 90
  2. 20
  3. 72
  4. 40
  5. 17
  6. 360
  7. 90
  8. 60
  9. 90
  10. 56
  11. 270
  12. 270
  13. 56
  14. 150
  15. 450
  16. 6
  17. 47
  18. 40
  19. 120
  20. 181
  21. 40
  22. 30
  23. 5
  24. 60
  25. 6
  26. 36
  27. 40
  28. 72
  29. 120
  30. 63
  31. 43
  32. 186
  33. 450
  34. 25
  35. 28
  36. 40
  37. 12
  38. 183
  39. 120
  40. 25

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