L.C.M of Decimal Numbers.

LCM of Decimals:

We need to make the same number of decimal places in all the given numbers; then find their LCM as if they were integers, and mark in the result as many decimal places as there are in each of the numbers.

1) 0.6, 9.6 and 0.36.

Answer:

The given numbers are 0.6, 9.6 and 0.36
(i) Converting the Decimal numbers to Like Decimals= 0.60 , 9.60 , 0.36

 Now, find the LCM of 60, 960 and 36 = 2880.

 

(ii)The decimal point is to be placed for the L.C.M.
∴ The required LCM = 28.80.

                         (or)

(i) Convert the given decimal numbers into Fractions:

0.6 = 6/10 ; 9.6 = 96/10 ; 0.36 = 36/100.

L.C.M ( x/a , y/b, z/c ) = L.C.M (x,y,z) / H.C.F ( a,b,c ).

Therefore, L.C.M( 6/10 , 96/10 , 36/100 )

= L.C.M(6,96,36) / H.C.F(10,10,100)

(ii) L.C.M(6, 96, 36) =  288.

      H.C.F(10,10,100) = 10.

(iii) L.C.M( 6/10 , 96/10 , 36/100 )

       =  288 / 10 = 28.8

 

2) 0.48, 0.72 and 0.108
Answer:

Given decimal numbers: 0.48, 0.72 and 0.108
Converting each of the following decimals into like decimals we get;
0.480, 0.720 and 0.108
Now, expressing each of the numbers without the decimals as the product of primes we get
480 = 2 × 2 × 2 × 2 × 2 × 3 × 5 = 2⁵ × 3 × 5
720 = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 2⁴ × 3² × 5
108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³
L.C.M. of 480, 720 and 108 = 2⁵ × 3³ × 5 = 4320
Therefore, L.C.M. of 0.48, 0.72, 0.108 = 4.32 (taking 3 decimal places)

                     (or)

(i) Convert the given decimal numbers into Fractions:

0.48 = 48/100 ; 0.72 = 72/100 ; 0.108 = 108/1000.

L.C.M ( x/a , y/b, z/c ) = L.C.M (x,y,z) / H.C.F ( a,b,c ).

Therefore, L.C.M( 48/100 , 72/100 , 108/1000 )

= L.C.M(48, 72, 108) / H.C.F(100,100,1000)

(ii) L.C.M(48, 72, 108) =  432.

      H.C.F(100,100,1000) = 100.

 

Therefore, L.C.M( 48/100 , 72/100 , 108/1000 )

= 432 / 100 = 4.32 .