The Least common Multiple (L.C.M) of 0.12, 9.60, 0.60 is:

The correct option is 9.60.

Step-by-Step Explanation:

To find the Least Common Multiple (L.C.M) of decimal numbers, we can express each decimal number as a fraction with a common denominator.

Step 1: Express the numbers with equal decimal places

The given numbers are:

$0.12$

$9.60$

$0.60$

Each number has 2 decimal places. Writing them as fractions over a common denominator of 100:

$0.12=\frac{12}{100}$

$9.60=\frac{960}{100}$

$0.60=\frac{60}{100}$

Step 2: Find the L.C.M of the numerators

Now, we find the L.C.M of the integers 12, 960, and 60 using prime factorization:

$12=2^2\times 3$

$60=2^2\times 3\times 5$

$960=2^6\times 3\times 5$

Taking the highest power of each prime factor:

$\text{L.C.M}(12,960,60)=2^6\times 3\times 5=64\times 15=960$

Step 3: Calculate the L.C.M of the original decimals

Divide the L.C.M of the numerators by the common denominator (100):

$\text{L.C.M}(0.12,9.60,0.60)=\frac{960}{100}=9.60$

Therefore, the Least Common Multiple of 0.12, 9.60, and 0.60 is 9.60.