Question
Tue March 23, 2010 By: Somya Pandey

How to find out if in a question the HCF or the LCM has to be found out?

Expert Reply
Wed March 24, 2010

Following are illustrative example, you can ask specific doubts.

Illustrative Examples

Example

Find the L.C.M. of 72, 240, 196.

Solution

Using Prime factorisation method
   72 = 2×2×2×3×3 = 2³×3²
   240 = 2×2×2×2×3×5 = 24×3×5
   196 = 2×2×7×7 = 2²×7²
L.C.M. of the given numbers = product of all the prime factors of each of the given number with greatest index of common prime factors
     = 24×3²×5×7² = 16×9×5×49 = 35280.

 

Example

Find the H.C.F. of 72, 126 and 270.

Solution

Using Prime factorisation method
    72 = 2×2×2×3×3 = 2³×3²
  126 = 2×3×3×7 = 21×3²×71
  270 = 2×3×3×3×5 = 21×3³×51
H.C.F. of the given numbers = the product of common factors with least index
  = 21×3² = 2×3×3 = 18

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