Given $3780=2^{2}\times 3^{a}\times 5\times 7^{b}$ when expressed as a product of its prime f

Question

Given $3780=2^{2}\times 3^{a}\times 5\times 7^{b}$ when expressed as a product of its prime factors. Write down the values of $a$ and of $b$. Hence, find the smallest positive integer value of $k$, when $3780k$ is a perfect square.

Accepted Answer

(a) $a=3,\ b=1$ (b) $105$

Prime Factorisation and Conditions for a Perfect Square

Prime Factorisation and Conditions for a Perfect Square

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