Question

The Least Common Multiple (LCM) of 0.12, 9.60, 0.60 is:
(a) 9.60
(b) 0.12
(c) 0.6
(d) None of these

Answer 1

Hint: First of all write all the numbers in the rational form by eliminating the decimal. Then separately take the prime factorization of numerator and the denominator and then in the final answer write the L.C.M of the numerator and the L.C.M of the denominator. This is how we are going to find the L.C.M of the given numbers.

Complete step by step solution:
The three numbers given in the above problem of which we have to find the L.C.M is as follows:
0.12, 9.60, 0.60
Now, converting the above decimals into the fraction form and that can be done when decimal is removed from each of the three expressions then we will divide each of the three numbers by 100 and the above numbers will look as follows:
$\dfrac{12}{100},\dfrac{960}{100},\dfrac{60}{100}$
Taking the prime factorization of all the three numerators of the above expression we get,
$\begin{align}
  & 12=2\times 2\times 3 \\
 & 960=2\times 2\times 2\times 2\times 2\times 2\times 3\times 5 \\
 & 60=2\times 2\times 3\times 5 \\
\end{align}$
Now, we are going to find the L.C.M of the above three numbers. For that, first of all, we will find the common factors in the above three numbers which are 12 then we will multiply the remaining factors which are not common in all the three numbers. The remaining factors in 960 are 80 and the remaining factors in 60 are 5. But the catch is that the 5 factor has come in 960 and 60 also so if we take the factor 5 separately then we will double count the factor 5 so dropping the factor 5 from 60. Now, multiplying 12 by 80 we get,
$\begin{align}
  & 12\times 80 \\
 & =960 \\
\end{align}$
From the above, we have found the L.C.M of the numerator as 960. Now, we are going to find the L.C.M of the denominator.
All the denominators of the three numbers are the same and are 100 so the L.C.M of the denominator is 100.
Now, writing the L.C.M of the numerator and the denominator we get,
$\begin{align}
  & \dfrac{960}{100} \\
 & =9.60 \\
\end{align}$
Hence, we got the L.C.M of the three numbers as 9.60

So, the correct answer is “Option A”.

Note: To get the correct L.C.M of the three given numbers make sure you have correctly written the prime factorization of the numerators. Also, correctly write the L.C.M of the numerator by not double counting the remaining factors from 60.