1.

Find the least square number which is exactly divisibleeach of thenumber 8, 9, 10 and 15.​

Answer»

Solution :

\bigstar Firstly, we get L.C.M of each number 8,9,10 & 15 ;

\begin{array}{r|l} <klux>2</klux> & 8,9,10,15 \\ \cline{2-2} 2 & <klux>4</klux>,9,5,15 \\ \cline{2-2} 2 & 2,9,5,15 \\ \cline{2-2} <klux>3</klux>& 1,9,5,15 \\ \cline{2-2} 3 & 1,3,5,5 \\ \cline{2-2} 5& 1,1,5,5 \\ \cline{2-2} & 1,1,1,1 \end{array}}

Prime factorization = 2 × 2 × 2 × 3 × 3 × 5

We should MULTIPLY by 2 & 5 to get complete square number.

Thus;

⇒ The required square number = 2² × 2² × 3² × 5²

⇒ The required square number = 4 × 4 × 9 × 25

⇒ The required square number = 3600


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