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# Find the L.C.M. of 2.5, 0.5 and 0.175.

Last updated date: 17th Jun 2024
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Hint: First remove the decimal by multiplying all the numbers with 1000. To balance, divide them with 1000. Leave the number 1000 in the denominator as it is and consider the numbers obtained in the numerator, find their L.C.M. by prime factorization method. Once the L.C.M. is found, divide it with 1000 to get the answer.

\begin{align} & \Rightarrow 2.5,0.5,0.175=\dfrac{2500}{1000},\dfrac{500}{1000},\dfrac{175}{1000} \\ & \Rightarrow 2.5,0.5,0.175=\dfrac{1}{1000}\left( 2500,500,175 \right) \\ \end{align}
\begin{align} & \Rightarrow 2500={{2}^{2}}\times {{5}^{4}} \\ & \Rightarrow 500={{2}^{2}}\times {{5}^{3}} \\ & \Rightarrow 175={{5}^{2}}\times 7 \\ \end{align}
$\Rightarrow L.C.M.={{2}^{2}}\times {{5}^{4}}\times 7$
\begin{align} & \Rightarrow L.C.M.=\dfrac{{{2}^{2}}\times {{5}^{4}}\times 7}{1000} \\ & \Rightarrow L.C.M.=17.5 \\ \end{align}
Note: One may note that the numbers 2.5 and 0.5 will get free form the decimal even after multiplying with 10, but the third number 0.175 will have to be multiplied with 1000 to get free from decimal and that is why we choose this number. You can note that the general method of finding the L.C.M. of two fractions $\dfrac{a}{b}$ and $\dfrac{c}{d}$ is that, first we find the L.C.M. of a and c, i.e., the numerators, then in the next step we find the H.C.F. of b and d, i.e., the denominators and finally we use the relation: - L.C.M. required = $\dfrac{L.C.M.\left( a,c \right)}{H.C.F.\left( b,d \right)}$, to get the answer.