L.C.M and H.C.F Shortcuts

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 score 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 the division method.

1) Find the LCM of 12, 17, 30 using the 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. The 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 of numbers would be either the smallest or lower than the smallest number.