L.C.M and H.C.F Shortcuts & Questions For PSC & UPSC Exams

If you are preparing for PSC and UPSC exams, one of the important section in quantitative aptitude is LCM and HCF. If you prepare properly, you can get 100 percent from this part. L.C.M. (Least Common Multiple) is the least non-zero number in common multiples of two or more numbers. H.C.F. (Highest Common Factor) is the highest common factor of two or more numbers which means the biggest number which divides each of them exactly. Now let us check some interesting facts and formulas which help you to solve any questions asked in competitive exams by Banks, CAT, state and central Governments etc.


Division Method to Find LCM and HCF

Before going for methods to solve LCM and HCF questions asked in aptitude examinations, let us check the methods to find these values using division method.

1) Find the LCM of 12, 17, 30 using division method

        | 
      2 |  12 , 17, 30
         --------------------- 
           |6, 17, 15
        2  |
            -------------------------------- 
            3 |3, 17,5
              |
               -----------------------  
                 1, 17, 5



   LCM = 2 X 2 X 3 X 17 X 5 = 1020


2 ) Find HCF of 24, 40, 64 using division method

        | 
      2 |  24 , 40, 64
         --------------------- 
           |12, 20, 32
        2  |
            -------------------------------- 
            2 |6, 10,16
              |
               -----------------------  
                 3, 5, 8

HCF = 2  X  2  X  2 = 8


Important Formulas to Solve Competitive Examination Questions

  1. Product of two numbers = Product of LCM and HCF of those numbers

    ie:
    P x Q = L x H       where L is LCM and H is HCF of two numbers P and Q.
    
    
    • LCM = (P x Q) / HCF
    • HCF = (P x Q) / LCM
    • P = (LCM  x  HCF ) / Q

  2. Find the LCM of fractions

    To find the LCM of fractions, divide the LCM of numerators by HCF of denominators


  3. Find the H.C.F. of fractions

    to find the H.C.F. of fractions, divide the H.C.F. of numerators by L.C.M. of denominators


Solved examples

1) H.C.F. of two numbers is 2 and L.C.M. is 180. One of the two numbers is 10. Find the second number.

According to our formula,  

     P = (LCM  x  HCF ) / Q   

     so P = (2 x 180 ) / 10  =36

    

The second number is 36.


Hints

  • If you are asked to find the least number divisible by a set of number, all you have to find is the L.C.M.

  • L.C.M. of a given set of numbers must be either the biggest number or bigger than the biggest number in the list

  • H.F.C. of a given set set of numbers would be either the smallest or lower than the smallest number.