2026 CCHMS P1 Q12

When written as products of their prime factors,

\(\begin{aligned} p&=2^3\times3^6 \\ q&=2\times3^2\times7 \\ r&=2^2\times3\times5 \end{aligned}\)

Find

1. the value of the cube root of \(p\),[1]
2. the lowest common multiple of \(p\), \(q\) and \(r\), giving your answer as a product of its prime factors.[1]
3. the greatest positive integer that divides \(p\), \(q\) and \(r\) exactly.[1]