Given $3780=2^{2} imes 3^{a} imes 5 imes 7^{b}$ when expressed as a product of its prime factors.

Question

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

Accepted Answer

(a) a = 3, b = 1, (b) k = 105

Prime Factorisation and Conditions for a Perfect Square

Prime Factorisation and Conditions for a Perfect Square

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