HCF and LCM Questions Answers

• 15. Find the largest number of four digits which is exactly divisible by 27,18,12,15

  1. 9700
  2. 9710
  3. 9720
  4. 9730

  Answer And Explanation

  Answer: Option C

  Explanation:

  LCM of 27-18-12-15 is 540.
  After dividing 9999 by 540 we get 279 remainder.
  So answer will be 9999-279 = 9720

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• 16. Six bells commence tolling together and toll at the intervals of 2,4,6,8,10,12 seconds resp. In 60 minutes how many times they will toll together.

  1. 15
  2. 16
  3. 30
  4. 31

  Answer And Explanation

  Answer: Option D

  Explanation:

  LCM of 2-4-6-8-10-12 is 120 seconds, that is 2 minutes.
  
  Now 60/2 = 30
  Adding one bell at the starting it will 30+1 = 31

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• 17. An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10 a.m. The time when they will next make a beep together at the earliest, is

  1. 10:28 am
  2. 10:30 am
  3. 10:31 am
  4. None of above

  Answer And Explanation

  Answer: Option C

  Explanation:

  L.C.M. of 60 and 62 seconds is 1860 seconds
  1860/60 = 31 minutes
  
  They will beep together at 10:31 a.m.
  
  Sometimes questions on red lights blinking comes in exam, which can be solved in the same way

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• 18. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is

  1. 16cm
  2. 25cm
  3. 15cm
  4. 35cm

  Answer And Explanation

  Answer: Option D

  Explanation:

  So by now, you must be knowing this is a question of HCF, right.
  H.C.F. of (700 cm, 385 cm, 1295 cm) = 35 cm.

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• 19. The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is

  1. 48
  2. 22
  3. 56
  4. 27

  Answer And Explanation

  Answer: Option A

  Explanation:

  Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
  So, the numbers 12 and 16.
  L.C.M. of 12 and 16 = 48.

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• 20. The H.C.F. and L.C.M. of two numbers are 12 and 5040 respectively If one of the numbers is 144, find the other number

  1. 400
  2. 256
  3. 120
  4. 420

  Answer And Explanation

  Answer: Option D

  Explanation:

  Solve this question by using below formula.
  Product of 2 numbers = product of their HCF and LCM
  
  144 * x = 12 * 5040
  
  x = (12*5040)/144 = 420

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• 21. Find the greatest number that will divide 400, 435 and 541 leaving 9, 10 and 14 as remainders respectively

  1. 19
  2. 17
  3. 13
  4. 9

  Answer And Explanation

  Answer: Option B

  Explanation:

  Answer will be HCF of (400-9, 435-10, 541-14)
  
  HCF of (391, 425, 527) = 17

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