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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 254 · 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 9 that leaves a remainder of 1 when divided by 6, 9 or 3.
  2. 2.Two tanks hold 35 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Three temple bells ring every 4, 10 and 30 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 15 that leaves a remainder of 2 when divided by 10, 5 or 15.
  5. 5.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 4 or 10.
  7. 7.Three temple bells ring every 8, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 12, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 5, 12 or 8.
  10. 10.Vivaan takes 45 seconds and Meera 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?
  11. 11.Two tanks hold 210 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Rahul takes 72 seconds and Saanvi 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?
  13. 13.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Three temple bells ring every 15, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Tara takes 90 seconds and Rahul 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?
  16. 16.Ananya takes 30 seconds and Arjun 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?
  17. 17.Zoya takes 36 seconds and Kavya 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?
  18. 18.Three temple bells ring every 9, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.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?
  21. 21.Two tanks hold 15 litres and 35 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 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Saanvi takes 45 seconds and Pooja 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?
  24. 24.Three temple bells ring every 9, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Kabir takes 75 seconds and Ananya 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?
  26. 26.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?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 9 or 12.
  28. 28.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 8, 10 or 6.
  29. 29.Manav takes 72 seconds and Nisha 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?
  30. 30.Three temple bells ring every 6, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Farhan takes 72 seconds and Isha takes 80 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?
  32. 32.Nisha takes 90 seconds and Ananya 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?
  33. 33.Rohan takes 50 seconds and Aditya 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?
  34. 34.Two tanks hold 125 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Three temple bells ring every 12, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 180 litres and 140 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 15 that leaves a remainder of 4 when divided by 12, 10 or 15.
  38. 38.Diya takes 50 seconds and Kabir 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?
  39. 39.Two tanks hold 75 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 4 or 8.

Answer key

  1. 19
  2. 5
  3. 60
  4. 32
  5. 12
  6. 62
  7. 40
  8. 60
  9. 124
  10. 180
  11. 30
  12. 360
  13. 28
  14. 90
  15. 720
  16. 120
  17. 180
  18. 72
  19. 20
  20. 6
  21. 5
  22. 56
  23. 270
  24. 90
  25. 600
  26. 5
  27. 183
  28. 122
  29. 144
  30. 60
  31. 720
  32. 180
  33. 150
  34. 25
  35. 120
  36. 20
  37. 64
  38. 300
  39. 25
  40. 25

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