Answer

Verified

373.5k+ views

**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.

**Complete step-by-step answer:**

Here, we have been provided with the numbers 2.5, 0.5 and 0.175 and we are asked to find their L.C.M. But first let us make the numbers free form decimal. Now, on observing the three numbers we can say that we have to multiply them with 1000 so that all of them become free from the decimal. To balance, we need to divide them with 1000. So, we get,

\[\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}\]

Since, 1000 was common in all the three numbers in the denominator so we have taken it aside. Now, what we will do is we will find the L.C.M. of 2500, 500 and 175 and divide it with 1000 to get the answer.

Now, let us use the method of prime factorization to get the L.C.M. of three numbers. The L.C.M. of these numbers will be the product of the highest power of each prime factor appearing. So, writing 2500, 500 and 175 as the product of its primes, we have,

\[\begin{align}

& \Rightarrow 2500={{2}^{2}}\times {{5}^{4}} \\

& \Rightarrow 500={{2}^{2}}\times {{5}^{3}} \\

& \Rightarrow 175={{5}^{2}}\times 7 \\

\end{align}\]

Clearly, we can see that the highest power of the prime factor 2 is 2, 5 is 4 and 7 is 1, so the L.C.M. of the above three numbers can be given as: -

\[\Rightarrow L.C.M.={{2}^{2}}\times {{5}^{4}}\times 7\]

Now, we have to divide this L.C.M. with 1000 to get the L.C.M. of initial three numbers 2.5, 0.5 and 0.175, so we get,

\[\begin{align}

& \Rightarrow L.C.M.=\dfrac{{{2}^{2}}\times {{5}^{4}}\times 7}{1000} \\

& \Rightarrow L.C.M.=17.5 \\

\end{align}\]

Hence, 17.5 is our answer.

**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.

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail