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Home » 2. Find the LCM and HCF of the following integers by applying the prime factorization method:(iii)     (iv)    
2. Find the LCM and HCF of the following integers by applying the prime factorization method:(iii)

    \[\mathbf{8},\text{ }\mathbf{9}\text{ }\mathbf{and}\text{ }\mathbf{25}\]

(iv)

    \[\mathbf{40},\text{ }\mathbf{36}\text{ }\mathbf{and}\text{ }\mathbf{126}\]

CBSE | Class 10 | Maths | RD Sharma | Real Numbers
2. Find the LCM and HCF of the following integers by applying the prime factorization method:(iii)

    \[\mathbf{8},\text{ }\mathbf{9}\text{ }\mathbf{and}\text{ }\mathbf{25}\]

(iv)

    \[\mathbf{40},\text{ }\mathbf{36}\text{ }\mathbf{and}\text{ }\mathbf{126}\]

Solution:

First,

find the prime factors of the given integers: 8, 9 and 25             

For,

    \[8\text{ }=\text{ }2\text{ }\times \text{ }2\text{ }x\text{ }2\]

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> 9\text{ }=\text{ }3\text{ }\times \text{ }3 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> 25\text{ }=\text{ }5\text{ }\times \text{ }5 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

                                                       

Now, L.C.M of

    \[8,\text{ }9\]

and

    \[25\text{ }=\text{ }{{2}^{3}}~\times \text{ }{{3}^{2}}~\times \text{ }{{5}^{2}}\]

                                   

    \[\therefore L.C.M\text{ }\left( 8,\text{ }9,\text{ }25 \right)\text{ }=\text{ }1800\]

                             

And,

    \[~H.C.F\text{ }\left( 8,\text{ }9\text{ }and\text{ }25 \right)\text{ }=\text{ }1~~~~~~~~~~\]

Solution:

First, find the prime factors of the given integers:

    \[40,\text{ }36\text{ }and\text{ }126\]

                

For

    \[,\text{ }40\text{ }=\text{ }2\text{ }x\text{ }2\text{ }x\text{ }2~\times \text{ }5\]

         

    \[36\text{ }=\text{ }2\text{ }x\text{ }2\text{ }x\text{ }3\text{ }x\text{ }3\]

    \[126\text{ }=\text{ }2\text{ }\times \text{ }3\text{ }\times \text{ }3\text{ }\times \text{ }7\]

                      

Now,

    \[L.C.M\text{ }of\text{ }40,\text{ }36\text{ }and\text{ }126\text{ }=\text{ }{{2}^{3}}~\times \text{ }{{3}^{2}}~\times \text{ }5\text{ }\times \text{ }7~~~~~~~~~~\]

    \[\therefore L.C.M\text{ }\left( 40,\text{ }36,\text{ }126 \right)\text{ }=\text{ }2520\]

And,

    \[H.C.F\text{ }\left( 40,\text{ }36\text{ }and\text{ }126 \right)\text{ }=\text{ }2\]

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