Question

What is the LCM of 0.25,0.1 and 0.125. Show with explanation.

Answer 1

Multiply everything by thousand to make into whole no. Then divide by factors.

2    100  250  125
2    50    125  125 
25  25     125  125
5     1        5      5
       1        1      1


Now that there are all ones in the end, multiply all the factors on the left.

This is 2*2*25*5
This equals to 500 .
We multiplied everything by 1000 in the beginning, so now we have to divide it by 1000. That then becomes 0.5. The lcm of 0.25, 0.1 and 0.125 is 0.5. 

Answer 2

          x = 0.25     y = 0.1     z = 0.125 

multiply with 4 :   4 x = 1      4 y = 0.4    z = 0.5
multiply with 10:   40 x = 10      40 y =  4        40 z  = 5

               LCM of  (40 x, 40 y, 40 z)  =  LCM of  ( 10,  4,  5)   =   20 

                      LCM of x, y , z   = 20/40  = 0.5
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Another method:

    x = 0.25 ,    y = 0.1       z = 0.125
         
           x = 2 z ,        x = 2.5 y   =>   2 x = 5 y
                
               2 x = 5 y = 4 z 

  This is the least as 2 and 5 are co-prime.     LCM = 2 x = 5 y = 4 z = 0.5