Question

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

Answer 1

Solve for LCM of given numbers

L.C.M. of rational numbers = L.C.M of numerators $÷$ H.C.F of denominators

The numbers are $\frac{25}{10},\frac{5}{10},\frac{175}{1000}$

L.C.M.$(5,25,175)$ by prime factorization method

$5=5\times 1$

$25=5\times 5$

$175=5\times 5\times 7$

$\Rightarrow$L.C.M.$(5,25,175)=5\times 5\times 7=175$

H.C.F.$(10,10,1000)$ by prime factorization method

$10=10\times 1$

$1000=10\times 10\times 10$

$\Rightarrow$H.C.F.$(10,10,1000)=10$

$\therefore$L.C.M.$(2.5,0.5,0.175)=\frac{175}{10}=17.5$
Hence, LCM of $2.5,0.5,0.175$ is $17.5$