Question

Find the least multiple of 1575 which is a perfect square.

• A. 11025
• B. 10045
• C. 6845
• D. 8925

Answer 1

The correct option is A 11025

Prime factorization of 1575:
$\begin{array}{cc}5& 1575\\ 5& 315\\ 3& 63\\ 3& 21\\ & 7\end{array}$

$1575=\underset{–}{5\times 5}\times \underset{–}{3\times 3}\times \underset{–}{7}InpairInpairNotinpair$

So, in order to make it a perfect square, we need to multiply 1575 with 7.
Hence, the least multiple of 1575 which is a perfect square = 1575 $\times$ 7 = 11025.